Laws of Exponents · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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The Laws of Exponents

Mathematics · Algebra · ages 12-14
Name ______________________   Date ____________

  1. Which expression has matching bases and division, so you can subtract its exponents?

    • 9⁶ ÷ 8²
    • 9⁶ ÷ 9²
    • 9⁶ × 9²
    • 9⁶ + 9²

  2. Why does 11² × 11⁴ equal 11⁶?

    • Each power has base 11, so multiply 2 and 4 to count eight factors.
    • Each power has base 11, so multiply the bases and add the exponents.
    • The product has two factors of 11 because 4 − 2 = 2.
    • The product has six factors of 11 because 2 + 4 = 6.

  3. What is 2³ × 2⁴ written as a single power of 2?

    2³×2⁴=?
    • 2⁷
    • 2¹²
    • 4⁷

  4. Any nonzero number raised to the power 0 equals 1.

    Circle one:   True   False

  5. Malik simplifies 4² × 4³ and writes 16⁵. What is the correct answer?

    • 4⁶
    • 4⁵
    • 16⁵

  6. Evaluate 5⁴ × 5⁻¹ ÷ 5¹. Give an ordinary number.

    Answer: ______________

  7. Which comparison is correct?

    • 3⁻¹ > 3⁻²
    • 3⁻¹ < 3⁻²
    • 3⁻¹ = 3⁻²
    • 3⁻¹ = −3

  8. 2⁻³ = 1/n. What is n?

    Answer: ______________

  9. Nora writes 7² × 7³ ÷ 7⁴ = 7⁹ because she calculates 2 + 3 + 4. Which exponent calculation corrects her mistake?

    • 2 + 3 − 4 = 1
    • 2 × 3 − 4 = 2
    • 2 + 3 + 4 = 9

  10. 2⁴ × 2⁻⁶ = 1/n. What is n?

    Answer: ______________

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Answer key

For grown-ups. Fold this page away before handing over the rest.

The Laws of Exponents W1-mt_UjNba32kkz-s1

  1. 9⁶ ÷ 9² · 9⁶ ÷ 9² has the same nonzero base in both powers and uses division. Its exponent becomes 6 − 2.
  2. The product has six factors of 11 because 2 + 4 = 6. · 11² contains two factors of 11 and 11⁴ contains four. Their product contains six factors of 11, which is 11⁶.
  3. 2⁷ · Add the exponents because the bases match: 3 + 4 = 7, so 2³ × 2⁴ = 2⁷.
  4. True · For a nonzero base a, a³ ÷ a³ equals 1. Subtracting the exponents gives a⁰, so a⁰ = 1.
  5. 4⁵ · The base stays 4; only the exponents add: 2 + 3 = 5, so 4² × 4³ = 4⁵, not 16⁵.
  6. 25 · Add −1 for multiplication and subtract 1 for division: 4 + (−1) − 1 = 2. The expression is 5² = 25.
  7. 3⁻¹ > 3⁻² · 3⁻¹ = 1/3 and 3⁻² = 1/9. One third is greater than one ninth, so 3⁻¹ > 3⁻².
  8. 8 · Use the reciprocal of the positive power: 2⁻³ = 1/2³ = 1/8. Comparing this with 1/n gives n = 8.
  9. 2 + 3 − 4 = 1 · Multiplication adds the exponent 3, but division subtracts the exponent 4. Calculate 2 + 3 − 4 = 1, giving 7¹ = 7.
  10. 4 · Add the exponents: 4 + (−6) = −2. Then 2⁴ × 2⁻⁶ = 2⁻² = 1/2² = 1/4, so n = 4.
Worksheet · LightMySky