Grade 8 Algebra: Word Problems: Exponents

Name: ______________________Date: ____________Score: ____ / 6

Level 1

Repeated multiplication

1. Solve:
$\text{A}$ $\text{bacteria}$ $\text{colony}$ $\text{doubles}$ $\text{every}$ $\text{hour.}$ $\text{It}$ $\text{starts}$ $\text{with}$ $\text{1}$ $\text{cell.}$ $\text{How}$ $\text{many}$ $\text{cells}$ $\text{are}$ $\text{there}$ $\text{after}$ $\text{5}$ $\text{hours?}$
2. Solve:
$\text{Write}$ $\text{3}$ $\text{times}$ $\text{3}$ $\text{times}$ $\text{3}$ $\text{times}$ $\text{3}$ $\text{as}$ $\text{a}$ $\text{power,}$ $\text{then}$ $\text{find}$ $\text{its}$ $\text{value.}$
3. Solve:
$\text{A}$ $\text{square}$ $\text{has}$ $\text{side}$ $\text{length}$ $\text{7}$ $\text{cm.}$ $\text{Find}$ $\text{its}$ $\text{area}$ $\text{as}$ $\text{a}$ $\text{power}$ $\text{and}$ $\text{as}$ $\text{a}$ $\text{number.}$
4. Solve:
$\text{A}$ $\text{cube}$ $\text{has}$ $\text{edge}$ $\text{length}$ $\text{4}$ $\text{cm.}$ $\text{Find}$ $\text{its}$ $\text{volume}$ $\text{as}$ $\text{a}$ $\text{power}$ $\text{and}$ $\text{as}$ $\text{a}$ $\text{number.}$
5. Solve:
$\text{Ana}$ $\text{tells}$ $\text{3}$ $\text{friends}$ $\text{a}$ $\text{secret.}$ $\text{Each}$ $\text{friend}$ $\text{tells}$ $\text{3}$ $\text{new}$ $\text{people,}$ $\text{and}$ $\text{each}$ $\text{of}$ $\text{those}$ $\text{tells}$ $\text{3}$ $\text{more.}$ $\text{How}$ $\text{many}$ $\text{people}$ $\text{hear}$ $\text{it}$ $\text{in}$ $\text{the}$ $\text{third}$ $\text{round?}$
6. Solve:
$\text{Leo}$ $\text{saves}$ $\text{1}$ $\text{coin}$ $\text{on}$ $\text{day}$ $\text{1}$ $\text{and}$ $\text{doubles}$ $\text{his}$ $\text{coins}$ $\text{each}$ $\text{day.}$ $\text{How}$ $\text{many}$ $\text{coins}$ $\text{does}$ $\text{he}$ $\text{save}$ $\text{on}$ $\text{day}$ $\text{8?}$

Answer Key

Level 1

1. $2^5 = 32$
2. $3^4 = 81$
3. $7^2 = 49\text{ cm}^2$
4. $4^3 = 64\text{ cm}^3$
5. $3^3 = 27$
6. $2^7 = 128$

Grade 8 Algebra: Word Problems: Exponents

Name: ______________________Date: ____________Score: ____ / 6

Level 2

Using the exponent rules

1. Solve:
$\text{A}$ $\text{box}$ $\text{holds}$ $10^{3}\text{}$ $\text{pencils.}$ $\text{A}$ $\text{store}$ $\text{has}$ $10^{4}\text{}$ $\text{boxes.}$ $\text{How}$ $\text{many}$ $\text{pencils}$ $\text{are}$ $\text{there}$ $\text{in}$ $\text{total?}$
2. Solve:
$\text{A}$ $\text{hard}$ $\text{drive}$ $\text{holds}$ $2^{30}\text{}$ $\text{bytes.}$ $\text{Each}$ $\text{file}$ $\text{uses}$ $2^{10}\text{}$ $\text{bytes.}$ $\text{How}$ $\text{many}$ $\text{files}$ $\text{fit?}$
3. Solve:
$\text{A}$ $\text{cube}$ $\text{has}$ $\text{edge}$ $\text{length}$ $3x^{}\text{.}$ $\text{Write}$ $\text{an}$ $\text{expression}$ $\text{for}$ $\text{its}$ $\text{volume.}$
4. Solve:
$\text{A}$ $\text{square}$ $\text{garden}$ $\text{has}$ $\text{side}$ $\text{length}$ $5^{2}\text{}$ $\text{meters.}$ $\text{Find}$ $\text{its}$ $\text{area.}$
5. Solve:
$\text{A}$ $\text{rumor}$ $\text{reaches}$ $\text{4}$ $\text{times}$ $\text{as}$ $\text{many}$ $\text{people}$ $\text{each}$ $\text{day.}$ $\text{On}$ $\text{day}$ $\text{1,}$ $\text{4}$ $\text{people}$ $\text{know}$ $\text{it.}$ $\text{How}$ $\text{many}$ $\text{know}$ $\text{it}$ $\text{on}$ $\text{day}$ $\text{5?}$
6. Solve:
$\text{Light}$ $\text{travels}$ $\text{about}$ $3\times 10^{5}\text{}$ $\text{km}$ $\text{per}$ $\text{second.}$ $\text{How}$ $\text{far}$ $\text{does}$ $\text{it}$ $\text{travel}$ $\text{in}$ $10^{2}\text{}$ $\text{seconds?}$

Answer Key

Level 2

1. $10^3 \cdot 10^4 = 10^7$
2. $\dfrac{2^{30}}{2^{10}} = 2^{20}$
3. $(3x)^3 = 27x^3$
4. $(5^2)^2 = 5^4 = 625\text{ m}^2$
5. $4^5 = 1024$
6. $3 \times 10^7\text{ km}$

Answer Key

Level 3

1. $64 \cdot \left(\tfrac{1}{2}\right)^4 = 4\text{ cm}$
2. $\dfrac{1}{10^{-6}} = 10^6$
3. $800 \cdot \left(\tfrac{1}{2}\right)^4 = 50\text{ mg}$
4. $2x^2$
5. $2^{10} = 1024 > 1000,\; \text{by } 24$
6. $0.1 \cdot 2^{10} = 102.4\text{ mm}$