Question

ections: Solve each problem. Show your work and write your final answer clearly.
1. A computer program increases data using powers of 2. One process multiplies the data by
23 and another multiplies it by 24. What is the simplified power of 2 that represents the total
increase?
Answer: _______________________________________________
2. A science lab tracks bacteria growth using powers of 5. The growth is represented by the
expression 56 ÷ 52. Simplify the expression using exponent rules.
Answer: _______________________________________________
3. A digital storage system updates its capacity using the expression (32)3. Simplify the
exponential expression.
Answer: _______________________________________________
4. A school is designing a square vegetable garden for students. The total area of the garden
will be 144 square feet. Because the garden is square, all sides are equal. What is the length
of one side of the garden?
Answer: _______________________________________________
5. The school is planning a larger square community garden behind the gym. The total area
of the garden will be 400 square feet. What is the length of each side of the garden?
Answer: _______________________________________________
6. The school gym stores equipment in cube-shaped storage containers. One container has a
volume of 64 cubic inches. What is the length of one edge of the cube-shaped container?
Answer: _______________________________________________
7. A fitness center stores medicine balls in cube-shaped bins. One bin has a volume of 343
cubic feet. What is the length of one side of the bin?
Answer: _______________________________________________
8. A square exercise mat in the gym covers an area of 196 square inches. What is the length
of one side of the mat?
Answer: _______________________________________________
9. A coach builds a cube-shaped box to hold training equipment. The box has a volume of
125 cubic inches. What is the length of one edge of the box?
Answer: _______________________________________________
10. Two numbers add up to 18. Their difference is 6. Write a system of equations and
determine the two numbers.
Answer: _______________________________________________
11. A school sold tickets to a basketball game. Student tickets cost $3 and adult tickets cost
$5. A total of 60 tickets were sold and the school collected $240. How many student tickets
and adult tickets were sold?
Answer: _______________________________________________
12. A farmer has chickens and goats in a field. There are 20 animals total and 64 legs
altogether. Chickens have 2 legs and goats have 4 legs. How many chickens and goats are
there?
Answer: _______________________________________________
13. Two friends are saving money for new gym shoes. Alicia starts with $10 and saves $4
each week. Brandon starts with $2 and saves $6 each week. After how many weeks will they
have the same amount of money?
Answer: _______________________________________________
14. Two gym membership plans charge different prices. Plan A costs $30 plus $5 per visit.
Plan B costs $10 plus $8 per visit. After how many visits will both plans cost the same

Answer 1

1. One process multiplies by 2^3 and the other by 2^4. Multiply the factors: 2^3 · 2^4 = 2^(3+4) = 2^7.
Answer: 2^7

2. 5^6 ÷ 5^2 = 5^(6−2) = 5^4 = 625.
Answer: 5^4 = 625

3. (3^2)^3 = 3^(2·3) = 3^6 = 729.
Answer: 3^6 = 729

4. Side length = √144 = 12.
Answer: 12 ft

5. Side length = √400 = 20.
Answer: 20 ft

6. Edge length = ∛64 = 4.
Answer: 4 in

7. Edge length = ∛343 = 7.
Answer: 7 ft

8. Side length = √196 = 14.
Answer: 14 in

9. Edge length = ∛125 = 5.
Answer: 5 in

10. Let the numbers be x and y.
x + y = 18
x − y = 6
Add: 2x = 24 ⇒ x = 12. Then y = 6.
Answer: 12 and 6

11. Let s = student tickets, a = adult tickets.
s + a = 60
3s + 5a = 240
s = 60 − a ⇒ 3(60 − a) + 5a = 240 ⇒ 180 − 3a + 5a = 240 ⇒ 2a = 60 ⇒ a = 30, s = 30.
Answer: 30 student, 30 adult

12. Let c = chickens, g = goats.
c + g = 20
2c + 4g = 64
c = 20 − g ⇒ 2(20 − g) + 4g = 64 ⇒ 40 − 2g + 4g = 64 ⇒ 2g = 24 ⇒ g = 12, c = 8.
Answer: 8 chickens, 12 goats

13. Alicia: 10 + 4w. Brandon: 2 + 6w.
10 + 4w = 2 + 6w ⇒ 8 = 2w ⇒ w = 4 weeks.
Answer: 4 weeks

14. Plan A: 30 + 5v. Plan B: 10 + 8v.
30 + 5v = 10 + 8v ⇒ 20 = 3v ⇒ v = 20/3 ≈ 6 2/3 visits.
Answer: 20/3 visits (about 6.67 visits)