A free printable worksheet that pairs with the Exponent Racer game. The worksheet prints first, and the answer key prints on its own page after it, so you can leave it off. To make a PDF, click Print and choose "Save as PDF."

Exponent Rules

Grades 6–8 · CCSS 6.EE.A.1, 8.EE.A.1 · Pairs with the Exponent Racer game

Name

Date

In 5³, 5 is the base and 3 is the exponent: 5³ = 5 × 5 × 5. Same base: multiply → add the exponents, divide → subtract them. Power of a power → multiply them. a⁰ = 1, and a⁻ⁿ = 1 / aⁿ.

Key vocabulary

base: the number being multiplied; in 4³, the base is 4
exponent: how many times the base is used as a factor; in 4³, the exponent is 3
power: a base with an exponent, like 4³
product of powers: same base, multiply: add the exponents (2³ · 2⁴ = 2⁷)
quotient of powers: same base, divide: subtract the exponents (5⁶ ÷ 5² = 5⁴)
power of a power: multiply the exponents ((3²)&sup4; = 3⁸)
zero exponent: any nonzero base to the zero power is 1 (7⁰ = 1)
negative exponent: means one over the positive power: 5⁻² = 1/5² = 1/25

Part A: Evaluate each power

1. 2⁵

2. 3⁴

3. 10³

4. 7⁰

5. 5¹

6. 4³

Part B: Write as a single power

7. 3² × 3⁴

8. 5⁷ ÷ 5³

9. (2³)²

10. 10⁸ ÷ 10²

11. (7²)⁴

12. 2³ × 2⁵ ÷ 2⁴

Part C: Zero and negative exponents (write as a fraction or whole number)

13. 5⁻²

14. 2⁻³

15. 3² × 3⁻⁵

16. 9⁴ ÷ 9⁴

Part D: Vocabulary and reasoning

17. In 6⁴, name the base and the exponent, and find the value of the power.

base exponent value

18. Find the mistake. Sam wrote 4³ = 12. What did Sam do wrong? What is the correct value?

Correct:

19. The distance from Earth to the Moon is about 4 × 10⁵ km. Write 10⁵ as a whole number, then write the distance as a whole number.

10⁵ = distance ≈ km

Answer Key: Exponent Rules

For the teacher

2·2·2·2·2 = 32
3·3·3·3 = 81
1,000
1 (any nonzero base to the zero power)
5
4·4·4 = 64
Add exponents: 3⁶
Subtract exponents: 5⁴
Multiply exponents: 2⁶ (= 64)
10⁶
7⁸
2^(3+5−4) = 2⁴ (= 16)
1 / 5² = 1/25
1 / 2³ = 1/8
3^(2−5) = 3⁻³ = 1 / 3³ = 1/27
9⁰ = 1
Base 6, exponent 4, value 6·6·6·6 = 1,296
Sam multiplied the base by the exponent (4 × 3). Correct: 4·4·4 = 64
10⁵ = 100,000; the distance is about 400,000 km

Common mistakes to watch for: multiplying base × exponent (#18), multiplying exponents in the product rule (3⁸ for #7), and reading a negative exponent as a negative number (−25 for #13). Exponent Racer's wrong answer choices are built from these same mistakes.