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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.

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
Play the game: studentmathgames.com/exponent-racer© 2026 Mr. H · Free for classroom use

Answer Key: Exponent Rules

For the teacher
  1. 2·2·2·2·2 = 32
  2. 3·3·3·3 = 81
  3. 1,000
  4. 1 (any nonzero base to the zero power)
  5. 5
  6. 4·4·4 = 64
  7. Add exponents: 36
  8. Subtract exponents: 54
  9. Multiply exponents: 26 (= 64)
  10. 106
  11. 78
  12. 2^(3+5−4) = 24 (= 16)
  13. 1 / 5² = 1/25
  14. 1 / 2³ = 1/8
  15. 3^(2−5) = 3⁻³ = 1 / 3³ = 1/27
  16. 9⁰ = 1
  17. Base 6, exponent 4, value 6·6·6·6 = 1,296
  18. Sam multiplied the base by the exponent (4 × 3). Correct: 4·4·4 = 64
  19. 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.

Full Teacher Guide: studentmathgames.com/exponent-racer/guide.html© 2026 Mr. H