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Negative Exponents Practice Worksheet

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Negative Exponents Practice Worksheet

Use the rule that a⁻ⁿ = 1/aⁿ for a ≠ 0. Rewrite answers with positive exponents unless a question asks for another form. Show your reasoning for written questions.

Choose the Equivalent Expression

Select the one correct answer for each question.

1.Which value is equal to 6⁻²?
  • −36
  • 1/12
  • 1/36
  • 36
2.Which expression is another way to write t⁻⁴, where t ≠ 0?
  • −t⁴
  • 1/t⁴
  • t/4
  • 4/t
3.Evaluate 3⁻³.
  • −27
  • 1/9
  • 1/27
  • 27
4.Which expression is equal to 1/r⁵, for r ≠ 0?
  • r⁵
  • −r⁵
  • r⁻⁵
  • 5r
5.Which value is equal to (−2)⁻³?
  • −1/8
  • 1/8
  • −8
  • 8

Rewrite and Simplify

Give each answer using positive exponents. Assume variables in denominators are non-zero.

6.Rewrite p⁻⁶ using a positive exponent.
7.Evaluate 7⁻² and write the result as a fraction.
8.Rewrite 3a⁻³b² with positive exponents.
9.Simplify (4m⁻²)(5m⁻³), then write the result with positive exponents.
10.Evaluate 10⁻⁴ as a decimal.
11.Simplify (q⁵ · q⁻⁸) ÷ q⁻¹ and express the answer with positive exponents.
12.Simplify (2x⁻²y)(3x⁴y⁻³) using positive exponents.

Connect the Forms

Match each expression in the left column with its equivalent in the right column. Use each choice once.

13.Match each expression to its equivalent.
  • 1. 2⁻³
  • 2. z⁻⁴
  • 3. 5⁻¹
  • 4. w² · w⁻⁵
  • C. 1/5
  • D. 1/w³
  • B. 1/8
  • A. 1/z⁴

Apply Your Understanding

Explain your thinking or show the steps that lead to each answer.

14.A lab sample has a width of 2⁻⁵ centimetres. Write this width as a fraction and as a decimal.
15.Simplify (k⁴ · k⁻⁷) ÷ k⁻². Give your answer using only positive exponents.
16.A student claims that 5⁻² equals −25 because the exponent is negative. Explain the mistake and state the correct value.

3 printable pages

  • Negative Exponents Practice Worksheet, page 1 of 3: Choose the Equivalent Expression, Rewrite and Simplify

    Page 1

  • Negative Exponents Practice Worksheet, page 2 of 3: Connect the Forms

    Page 2

  • Negative Exponents Practice Worksheet, page 3 of 3: Apply Your Understanding

    Page 3

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