The actual yearly cost of the membership if club purchases for the year is $40
What is actual yearly cost of the membership of the club?
The annual membership cost of Membership warehouse clubs is modelled based on the fact that yearly fee is $100 and that 4% is given off purchases the member make in the course of year, hence, the actual yearly cost is modelled as shown below:
y=100−0.04x
y= actual yearly cost of the membership=unknown
x=cost of purchases in the year=$1,500
y=100-0.04($1500)
y=100-60
y=actual yearly cost of the membership =$40
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Full question:
Membership warehouse clubs offer shoppers low prices, along with rewards of cash back on club purchases. If the yearly fee for a warehouse club membership is $100 and the reward rate is 4%
on club purchases for the year, then the linear equation
y=100−0.04x models the actual yearly cost of the membership y, in dollars. Here x represents the yearly amount of club purchases, also in dollars.
a) Determine the actual yearly cost of the membership if club purchases for the year are $1500.
Find the product of 2√/18 and 2√5 in simplest form. Also, determine whether the
result is rational or irrational and explain your answer.
2√10/3 is irrational number
The term "rational number" refers to any number that can be stated as a fraction, as well as a positive, negative, or zero. If q is not equal to zero, it can be expressed as p/q.
The word "rational" is derived from the word "ratio," which is a fraction and really refers to a comparison of two or more values or integer numbers. It is the ratio of two integers, to put it simply.
Consider the rational integer 3/2. It denotes that the integer 3 is divided by the number 2.
Irrational numbers are those that are not rational in nature. Let's explain; irrational numbers can be expressed as decimals but not as fractions, hence they cannot be expressed as the ratio of two integers.
After the decimal point, irrational numbers have an infinite amount of non-repeating digits. Here's an illustration of an irrational number:
For instance, 8 = 2.828
MULTIPLYING THE TWO NUMBERS,
2/√18 x 2√5
= 2 /3√2 x 2√5
= 4√5/3√2
= 2√2 x √5 /3
= 2√10/3
rational number multiplied by an irrational number is always a irrational number.
Since √10 is a irrational number, therefore, 2√10/3 is irrational number.
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В
2x – у = 3
19x - 6y = 6
Answer:
work is shown and pictured
which expressions below equal a rational number? select all that apply.
The expressions that are equal to a rational number are [(2/3)+(4/5)], [(√3) - (√3)], and [(√49)(√1)].
A rational number is one that can be stated as the ratio of two numbers, with the denominator not equal to zero.All real numbers that are not rational numbers are referred to as irrational numbers. The ratio of two integers cannot be used to express irrational values.(a) π√4π√4 is equal to 2π, which is an irrational number.(b) (2/3)+(4/5)(2/3)+(4/5) = (22/15), which is a rational number.(c) (√36)-(√5)(√36)-(√5) = 6-√5, which is an irrational number.(d) (√3)-(√3)(√3)-(√3) = 0, which is a rational number.(e) (√49)(√1)(√49)(√1) = 7*1 = 7, which is a rational number.To learn more about real numbers, visit :
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The function ƒ(x) = e2x+1 when graphed could be described as
The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.
How to Interpret Exponential Graphs?The graphs of exponential functions are nonlinear—because their slopes are always changing, they look like curves, not straight lines.
Now, we are given the exponential function as; ƒ(x) = e^(2x + 1)
Now, as the exponent increases, the curves get steeper and the rate of growth increases respectively. Thus, we can see that the exponent we are given increases as seen in the exponent attached to it.
Thus, we can conclude that The function ƒ(x) = e^(2x + 1) when graphed could be described as; an increasing exponential graph.
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Explain the difference between ethics and security. are they related? if so, how?
Information security and ethics is defined as an all encompassing term that refers to all activities needed to secure information and systems that support it in order to facilitate its ethical use
ETHICS:
Derived from the Greek word “ethos”, which means “way of living”, ethics is a branch of philosophy that is concerned with human conduct, more specifically the behaviour of individuals in society. Ethics examines the rational justification for our moral judgments; it studies what is morally right or wrong, just or unjust.
In a broader sense, ethics reflects on human beings and their interaction with nature and with other humans, on freedom, on responsibility and on justice. It can be said that in general, ethics is concerned with human independence when it focuses on the relationship that exists between humans and the world
This independence is the primary condition in ethical decision-making and in any objective analysis of the facts. Individuals demonstrate independence when, in a decision-making process, they choose to free themselves as much as possible from their conditioning. Insofar as this operation assumes a degree of lucidity that allows us to judge objectively and to decide what direction to take, it will be understood that making ethical decisions is difficult.
SECURITY:
Security for information technology (IT) refers to the methods, tools and personnel used to defend an organization's digital assets. The goal of IT security is to protect these assets, devices and services from being disrupted, stolen or exploited by unauthorized users, otherwise known as threat actors. These threats can be external or internal and malicious or accidental in both origin and nature.
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Abby bakes 5 cupcakes. Esteban bakes 4 cupcakes. They put 3 candy hearts on each cupcake. How many candy hearts are used? Explain
Answer:2
Step-by-step explanation:
which of the following pairs of ratios form a proportion? a. 9 boys to 5 girls and 12 boys to 8 girls
Answer:
12 to 8
Step-by-step explanation:
cuz i am smart pls mark me brainliest
Siobhan’s team is solving the following equation: . Amalia says there are no solutions. Brian says there is one solution, but it is imaginary. Cristina says there are two solutions! Help them out. Determine the solution(s) and justify your answer. You may want to refer to the Math Notes box in Lesson 2.2.2 for help.
There is no real solution of given equation.
There is a special case that will tell us if a quadratic has no real solution: if b = 0 when a and c share the same sign (both positive or both negative), then there will be no real solution. The quadratic formula becomes much simpler when b = 0.
given equation [tex]x^{2} =-16[/tex]
[tex]x=\sqrt{-16},\:x=-\sqrt{-16}[/tex]
[tex]x=4i, x=-4i[/tex]
we get imaginary solutions of given equation
so, there is no real solution equation is exist.
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I need help fast please and thank you
Answer:
its the second option
Step-by-step explanation:
u can search for the formula for a right trapezoid and then solve it
Isabella needed to get her computer fixed. She took it to the repair store. The
technician at the store worked on the computer for 4.25 hours and charged her $144
for parts. The total was $547.75. Which equation or tape diagram could be used to
represent the context if a represents the cost of labor per hour?
The equation is 547.75 = 4.25a + 144 so the tape diagram in option D is the correct answer.
What is an equation?A mathematical equation that represents the relationship of two expressions on either side of the sign.
It has one or more variables and equal to symbol.
Example: 3x – 5 = 5
We have,
Time spent fixing the computer = 4.25 hours
Cost of parts = $144
Total cost = $547.75
Cost of labor per hour = a
Since the cost of labor per hour is 'a' cost of labor for 4.25 hours is:
= 4.25 x a
= 4.25a
We can write an equation as:
547.75 = 4.25a + 144
Thus the tape diagram in option D is the correct answer.
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<6 and <7 form a linear pair. Twice the measurement of <6 is twelve more than four times the measurement of <7. Find the measurement of each angle.
A linear pair , m∠7 = 58°, m∠6 = 122° are the measurement of each angle.
What is Linear Pair?
When two lines cross at one point, a linear pair of angles is created. If the angles follow the intersection of the two lines in a straight line, they are said to be linear. A linear pair's total angles are always equal to 180°.
Linear Pairs add up to equal 180°.
Step 1: Define
m∠6 + m∠7 = 180°
2m∠6 = 4m∠7 + 12
Step 2: Rewrite systems of equations
I will set m∠6 = x and m∠7 to y
x + y = 180°
2x = 4y + 12
Step 3: Rewrite 2nd equation
2x = 2(2y + 6)
x = 2y + 6
Step 4: Use Substitution
2y + 6 + y = 180
3y + 6 = 180
3y = 174
y = 58°
Step 5: Find x by plugging y back into an original equation
x + 58 = 180
x = 122°
Step 6: Rewrite
x = m∠6
y = m∠7
m∠6 = 122°
m∠7 = 58°
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A pilot flew a jet from City A to City B, a distance of 2000 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 9 h 10 min. What was the speed from City A to City B?
A pilot flew a jet from City A to City B, a distance of 2000 mi. On the return trip, the average speed was 20% faster than the outbound speed. The round-trip took 9 h 10 min. What was the speed from City A to City B?
Regular insulin is ordered iv at 7 units/hour. the iv bag contains 100 units of regular insulin in 100ml of d5w. the iv rate should be how many ml/hr? (round to the nearest whole number
The iv (insulin rate) rate should be 7 ml/hr.
Here,
Regular insulin is ordered iv at 7 units/hour.
The iv bag contains 100 units of regular insulin in 100ml of d5w.
We have to find the iv rate.
What is insulin rate?
Basal insulin rate is the rate at which an insulin pump provides small, “background” doses of fast-acting insulin.
Now,
Regular insulin is ordered iv at 7 units/hour.
The iv bag contains 100 units of regular insulin in 100ml of d5w.
The insulin rate in ml/hr = ( 7 units / 1 hr ) * (100 ml / 100 units) = 7 ml/hr
So, The iv (insulin rate) rate should be 7 ml/hr.
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Gabriel is deciding between two different movie streaming sites to subscribe to. Plan 1 cost $22 per month plus $1 per movie watched. Plan 2 cost $14 per month plus $3 per movie watched. Create a system of equations to represent this situation. Explains how many movies, x, would cause the two plans to have an equal monthly cost.
The number of movies that would make the monthly cost equal is 4.
What is the number of movies when the plans' cost would be equal?The total monthly cost is a function of the cost per month, total movies watched and the cost per movie.
The equations that represent the total cost of using the streaming sites would be in the form:
Total cost = cost per month + (number of movies watched x cost per movie)
Plan 1: $22 + ($x)
Plan 2: $14 + (3x)
When both plans have the same monthly cost, the two above equations would be equal
$22 + x =$14 + 3x
In order to determine the value of x, take the following steps:
Combine similar terms: $22 - $14 = 3x -x
Add similar terms together: $8 = 2x
Divide both sides of the equation by 2: $8 /$ 2 = x
x = 4
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-1/2 is equivalent to 1/2
Answer: No
Step-by-step explanation:
No because its off by 1 point, -1/2, 0, 1/2
Solve the following inequalities:
|x+2|<|x+1|
|x^2 + x -12|=x^2 +2x -6
|x-5|+|x+2|<8
The values of x are 3/ 2, 6 and 1/ 2 respectively.
How to solve the inequalitiesGiven the inequalities;
|x+2| < |x+1||x^2 + x -12| = x^2 +2x - 6|x-5| + |x+2| < 8|x+2| < |x+1|
collect like terms
|x + x| < |1 + 2|
add like terms
|2x| < |3|
Make 'x' the subject
|x| < |3/ 2|
|x^2 + x -12| = x^2 +2x - 6
Take the absolute values of the expression
x² + x + 12 = x² + 2x - 6
collect like terms
x² - x² + x - 2x = -6 + 12
- x = 6
x = 6
|x-5|+|x+2|<8
Take absolute values
x + 5 + x + 2 < 8
collect like terms
2x + 7 < 8
2x < 8 - 7
Make 'x' the subject
x < 1/ 2
Thus, the values of x are 3/ 2, 6 and 1/ 2 respectively.
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Match the mathematical expression with its translation.
1 .
x divided by y
6 x = y
2 .
the product of two numbers
x + y = 6
3 .
x subtracted from y
4 .
the sum of two numbers is six
x + y
5 .
the product of two numbers is six
x - y
6 .
x minus y
y = x - 6
7 .
the sum of x and y
xy
8 .
six times a number equals y
y ÷ x
9 .
y divided by x
y - x
10 .
six less than a number is y
xy = 6 HELP...
Answer:
x divided by y - x/y
the product of two numbers - xy
x subtracted from y - y-x
the sum of two numbers is six - x+y=6
the product of two numbers is six - xy=6
x minus y - x-y
the sum of x and y - x+y
six times a number equals y - 6x=y
y divided by x - y divided by x
six less than a number is y - y=x-6
Step-by-step explanation:
Solve the equation, and enter the solutions from least to greatest. If there is only one solution, enter "n.a." for the second solution. or Reset Nextelect the correct answer from each drop-down menu. Consider this expression. The simplest form of the expression has in the numerator and in the denominator. 1/x+1/x-10=x-9/x-10
We need to know how to solve quadratic equation for this problem. The solution of the equation is x=1 and x=10.
An equation that has a variable with maximum degree two is called a quadratic equation. A quadratic equation can be solved by factorization method. Factorization method is a method where we group the variables together to find common factors among them. The common factors give the solution of the equation. Since a quadratic equation has variable of degree two it has two solutions. The roots of a quadratic equation can be real and unequal, real and equal or imaginary. If we solve the given equation we get a quadratic equation.
[tex]\frac{1}{x} +\frac{1}{x-10} =\frac{x-9}{x-10} \\\frac{x-10+x}{x(x-10)} =\frac{x-9}{x-10} \\2x-10=x(x-9)\\2x-10=x^{2} -9x[/tex]
[tex]x^{2} -9x-2x+10=0\\x^{2} -11x+10=0\\x^{2} -10x-x+10=0\\x(x-10)-1(x-10)=0\\(x-1)(x-10)=0\\[/tex]
Therefore the solution of the equation is x=1 and x=10.
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Shifting data, by adding a constant to each data value, does not change the _________.
A. quartiles
B. mean
C. standard deviation
D. median
The standard deviation is a measure of a collection of values' variance or dispersion. The correct option is C, standard deviation.
What is a standard deviation?The standard deviation is a measure of a collection of values' variance or dispersion. A low standard deviation implies that the values are close to the set's mean, whereas a high standard deviation shows that the values are spread out over a larger range.
Shifting data, by adding a constant to each data value, do not change the standard deviation. This is because the standard deviation is a measurement of how much a group of values varies or is dispersed.
Hence, the correct option is C, standard deviation.
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1. Latoya earns $1.75 an hour for each child she baby-sits. How much does she earn if she baby- sits 3 children for 4 hours?
2. James works at a department store and receives a 25% discount on his purchases. He purchases some new clothes at the store and his total before the discount is $145.20. What is James's total after the discount?
3. Kegan borrows $78 from his sister. He will pay her back over a 4-week period. If he pays the same amount each week, how much will he have paid back after the third week?
4. Ashley stops by the grocery to pick up a few items. She buys a loaf of bread for $1.09, a pound of turkey for $4.59, 2 cans of soup for $0.79 each, and 4 oranges for $0.27 each. How much money does Ashley spend at the grocery?
5. Jackie buys a one-way ticket to Nevada and a one-way ticket back home. Each way costs $118. Joe buys a round-trip ticket to Nevada for $227. Whose ticket is less? By how much?
Cost price is also known as CP. cost price is the original price of an item. The cost is the total outlay required to produce a product or carry out a service. Cost price is used in establishing profitability in the following ways: Selling price (excluding tax) less cost results in the profit in money terms.
A "selling price" is the price that the seller gives. something that he/she wants or is offering to sell. The item has not been sold. yet. A "sale price" could be the price that was actually paid by a buyer
1.
she earns if she babysits 3 children for 4 hours= $63.
solution :
Given :
Latoya earns $1.75 an hour for each child she babysits
Total Number of babysitting hours for 3 child= 3x12=36 hours
let,
Total amount earned by Latoya: S
S= 36x1.75
S= $63
she earns if she babysits 3 children for 4 hours= $63.
2.
James's total after the discount = $108.75
Given :
his total before the discount is $145.20
receives a 25% discount on his purchases
Solution :
Buy price = MRP X DISCOUNT /100
Let the Buying price is c
c = 145x25/100
c = 145/4
c= $ 36.25
= MRP - DISCOUNT
Let James's total after the discount = p
p= 145-36.25
p= $108.75
3.
paid back after the third week= 19.5
Given :
Kegan borrows $78 from his sister.
Time = 4 week
each week Payment = 78/4=19.5
paid back after the third week= 19.5
4.
Ashley spends at the grocery= $8.34
Solution :
a loaf of bread = $1.09,
a pound of turkey = $4.59,
2 cans of soup =2x$0.79 each=$ 1.58
4 oranges = $0.27 x4= $1.08
Ashley spend at the grocery= 1.09 + $4.59, +$ 1.58+ $1.08 =$ 8.34
Ashley spends at the grocery= $8.34
5.
joe ticket is less Jackie's by 236-227= $9
Solution :
Jackie buys a one-way ticket to Nevada=$118
a one-way ticket back home=$118
Total = $118x2 =$236
But
Joe buys a round-trip ticket to Nevada for $227
joe ticket is less Jackie's by 236-227= $9
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The mean exam score for the first group of twenty examinees applying for a security job is 35.3 with a standard deviation of 3.6.
The mean exam score for the second group of twenty examinees is 34.1 with a standard deviation of 0.5. Both distributions are close to symmetric in shape.
Use the mean and standard deviation to compare the scores of the two groups.
The scores of two groups can be compared using coefficient of variation;
Coefficient of variation (C.V.) = (Standard Deviation/ Mean) × 100%;
For Data set 1;
Standard deviation = 3.6
Mean = 35.3
C.V. = (3.6/35.3) × 100%;
= 10.19%
For Data set 2;
Standard deviation = 0.5
Mean = 34.1
C.V. = (0.5/34.1) × 100%;
= 1.46%
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12. FIND THE ERROR A student is finding the
total cost c, including sales tax, of a book
that costs $9.95. The sales tax rate is 9%.
Find the student's mistake and correct it.
Here is what the student wrote (re-pasting for clarity)
C = 1.9 x 9.95
C = 18.91
C = $18.91
The error happens in the 1st line
Why? Because the 1.9 should be 1.09
The 1.9 represents a tax of 90% when we want a 9% tax instead
In other words, 9% = 9/100 = 0.09 while 90% = 90/100 = 0.9
-----------------
This is what the steps should look like
C = 1.09 x 9.95
C = 10.8455
C = 10.85
Don't forget to round to the nearest hundredth, aka nearest penny.
The total cost, after sales tax, is $10.85
x^5y^5z^3 =?
A. bases are different, so this can't be done.
B. xy5z3
C. (xy)5z3
To simplify the indices expression x⁵y⁵z³, we can conclude that; A. bases are different, so this can't be done.
How to simplify Indices?We want to simplify the indices given as;
x⁵y⁵z³
Now, we can see that the bases are different and as such it means they cannot be simplified using laws of indices on the exponents.
This is because when the bases are different, the expression cannot be factored with the exponents being added, subtracted, divided or multiplied.
Thus, we will conclude that the bases are different, so this can't be done.
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EASY LOOKING FOR ANSWER HELP
Answer:
I forgot the answer
Step-by-step explanation:
3.2*10^8, 1.2*10^8, 7*10^5, 5*10^3
At a cross-country track meet, Alicia ran 8 mph for the first part of the race, then increased her speed to 12 mph for the second part. If the race was 21 miles long and Alicia finished in 2 hours, how far did she run at the faster pace?
She ran 15 miles at a quicker speed based on the information supplied. See explanation below. This is a distance time problem.
What is the justification for the above result?The distances between the two "half" of the race are our unknowns here. We must assign them to variables - Alicia ran x miles in the first half of the race and y miles in the second.
Since the race is 21 miles in total, x and y together must add up to 21.
Hence,
x + y = 21
The speeds at which she raced and the total time involved are then given; we can link this to the distances using the speed and distance equation
d = st, or t = d/s.
Because she completed in two hours, the hours spent running the first and second parts must sum up to two hours, or:
x/8 + y/12 = 2
Two equations are sufficient to solve for two unknowns. We can approach this by multiplying the second equation by the LCM, 24
3x + 2y = 48
And rearrange the first to get y = 21 - x, which we can plug into the above. This gives us:
3x + 2(21 - x) = 48
3x + 42 - 2x = 48
x = 6
Use y = 21 - x again:
y = 21 - (6) = 15.
Recall that the question asks how long she ran at the faster speed - this would be the second half of the race, which we've labeled y, so 15 miles. But first, let's make sure our solution works.
Obviously, 15 + 6 = 21, thus the overall distance is correct.
In terms of time, 6 miles at 8 mph takes
6/8 =.75 hours = 45 minutes, whereas
15 miles at 12 mph takes 15/12 = 1.25 hours = 75 minutes.
As stated in the question, the total time to complete would be.
75 + 1.25 = 2 hours.
As a result, this solution is correct, as Alicia ran 15 miles at a quicker rate.
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2. The daily changes in four stock prices are shown in the table. Write
the changes from least to greatest in fraction form with a common
denominator.
Stock
-2 35/100
-1.64
2.05
1 9/40
We get the fractions in ascending order as -2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000.
We are given the daily changes in four stock prices as shown in the table.:
-2 35/100
-1.64
2.05
1 9/40
We have to arrange them from least to greatest in fraction form with a common denominator.
We can write -2 35/100 as:
-235 / 100 ( mixed fraction converted into the improper fraction)
= -2350 / 1000
We can write -1.64 as:
- 1.64 = -164 / 100 ( decimal into fraction)
= -1640 / 1000
We can write 2.05 as:
2.05 = 205 / 100 (decimal into fraction)
= 2050 / 1000
We can write 1 9/40 as:
1 9/40 = 49 / 40 ( mixed fraction converted into the improper fraction)
49 / 40 × 25 / 25
= 1225 / 1000
Arranging it from least to greatest, we get that:
-2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000
Therefore, we get the fractions in ascending order as -2350 / 1000, -1640 / 1000, 1225 / 1000 and 2050 / 1000.
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Please help me out with 3 questions..
Each part of the question is plotted on the number line as an image with the solution.
How are rational numbers represented on the number line?
On the number line, rational numbers could be represented. Origin refers to the numeric line's center (O). The illustration of rational numbers shows positive numbers here on the right side of zero, or the origin, and negative numbers on the left. Depending on the kind of fraction, rational numbers are represented differently on the number line.(1) [tex]\frac{-3}{8} , 1\frac{1}{5} = \frac{6}{5} = 1.2 , \frac{-3}{4}[/tex] are plotted on the number line as an image with the solution.
(2) -13+15+(-8) = -6 is plotted on the number line as an image with the solution.
(3) [tex]\frac{3-(-14)}{7} = \frac{17}{7} = 2.429, \frac{-36+58}{-11} = -2[/tex] are plotted on the number line as an image with the solution.
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marie deposits $1,650 for three years at 3% interest compounded daily what is her ending balance
Answer:
1805.38
Step-by-step explanation:
hope this helps
If Bill wants to find the average of his family's heights. If his brother is 60 inches tall, his
sister is 58 inches tall, his mother 64 inches tall, and his father 72 inches tall, how tall
does Bill need to be to have an average family height of at least 62 inches?
Answer: 56 inches
Step-by-step explanation:
a. 60+58+64+72=254 (Add the average of his family without including him)
a. 62x5=310 (The average times 5, cause there are 5 of them will get you the total number of inches)
b. 310-254=56 (Subtract the total number of the 5 of them with the 4 of them to find Bill's height)
you can check your answer by adding all their heights.
Please help me!
1. Simplify 5 to the 5th over 5 to the 8th. (4 points)
1 over 5 to the 3rd power
53
1 over 25
1 over 5 to the negative 3rd
2. Simplify 5 to the negative 4th power over 5 to the 3rd. (4 points)
57
5−1
1 over 5
1 over 5 to the 7th power
3. Simplify 4 to the 7th over 5 squared all raised to the 3rd power. (4 points)
4 to the 10th over 5 to the 5th
4 to the 4th over 5
4 to the 21st over 5 to the 6th
12 to the 7th over 15 squared
4. In which expression should the exponents be multiplied? (4 points)
one fifth to the 2nd times one fifth to the 6th
9 to the 3rd over 9 to the 4th
73 ⋅ 78
(26)−5
5. Which expression is equivalent to (53)−2? (4 points)
1 over 5 to the 3rd
negative 1 over 5 times 5 times 5 times 5 times 5 times 5 times
53
1 over 5 times 5 times 5 times 5 times 5 times 5 times
Answer:
[tex]\textsf{1.} \quad \dfrac{1}{5^5}[/tex]
[tex]\textsf{2.} \quad \dfrac{1}{5^7}[/tex]
[tex]\textsf{3.} \quad \dfrac{4^{21}}{5^{6}}[/tex]
[tex]\textsf{4.} \quad \left(2^6\right)^{-5}[/tex]
[tex]\textsf{5.} \quad \dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]
Step-by-step explanation:
Question 1
[tex]\textsf{Given}: \quad \dfrac{5^5}{5^8}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \dfrac{5^5}{5^8}=5^{(5-8)}=5^{-3}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies 5^{-3}=\dfrac{1}{5^3}[/tex]
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Question 2
[tex]\textsf{Given}: \quad \dfrac{5^{-4}}{5^3}[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \dfrac{5^{-4}}{5^3}=5^{(-4-3)}=5^{-7}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies 5^{-7}=\dfrac{1}{5^7}[/tex]
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Question 3
[tex]\textsf{Given}: \quad \left(\dfrac{4^{7}}{5^2}\right)^3[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \left(\dfrac{4^{7}}{5^2}\right)^3=\dfrac{4^{(7 \cdot 3)}}{5^{(2 \cdot 3)}}=\dfrac{4^{21}}{5^{6}}[/tex]
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Question 4
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies \left(\dfrac{1}{5}\right)^2 \cdot\left(\dfrac{1}{5}\right)^6=\left(\dfrac{1}{5}\right)^{2+6}=\left(\dfrac{1}{5}\right)^8[/tex]
[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]
[tex]\implies \dfrac{9^3}{9^4}=9^{(3-4)}=9^{-1}=\dfrac{1}{9}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^b \cdot a^c=a^{b+c}:[/tex]
[tex]\implies 7^3 \cdot 7^8=7^{(3+8)}=7^{11}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \left(2^6\right)^{-5}=2^{(6 \cdot -5)}=2^{-30}=\dfrac{1}{2^{30}}[/tex]
Therefore, the expression in which the exponents should be multiplied is (2⁶)⁻⁵.
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Question 5
[tex]\textsf{Given}: \quad \left(5^3\right)^{-2}[/tex]
[tex]\textsf{Apply exponent rule} \quad (a^b)^c=a^{bc}:[/tex]
[tex]\implies \left(5^3\right)^{-2}=5^{(3 \cdot -2)}=5^{-6}[/tex]
[tex]\textsf{Apply exponent rule} \quad a^{-n}=\dfrac{1}{a^n}:[/tex]
[tex]\implies 5^{-6}=\dfrac{1}{5^6}=\dfrac{1}{5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 \cdot 5 }[/tex]