Fractional Indices and Roots · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Roots wearing index outfits

Mathematics · Number Representation & Place Value · ages 15-16
Name ______________________   Date ____________
  1. What is 8^(2/3)?

    Answer: ______________

  2. What is 27^(1/3)?

    Answer: ______________

  3. What is 27^(1/3)?

    Answer: ______________

  4. 32^(1/5) equals 2.

    Circle one:   True   False

  5. What is 16^(3/4)?

    Answer: ______________

  6. What is 16^(3/4)?

    Answer: ______________

  7. What is 4^(-1/2)? Give your answer as a decimal.

    Answer: ______________

  8. What is 81^(3/4)?

    Answer: ______________

  9. What is 25^(-3/2)? Give your answer as a decimal.

    Answer: ______________

  10. What is 4^(-1/2)? Give a decimal.

    Answer: ______________

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Answer key

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

Roots wearing index outfits W1-mt_fdK-nbQcBu-s1

  1. 4 · Take the root first using the denominator, then apply the power from the numerator.
  2. 3 · A power of 1/3 means the cube root. You want the number that, multiplied by itself three times, gives 27.
  3. 3 · A power of 1/3 is the cube root, and 3 times 3 times 3 is 27.
  4. True · The fifth root of 32 is 2, since 2 to the power 5 is 32.
  5. 8 · Fourth root of 16 is 2, then 2 cubed is 8.
  6. 8 · The denominator of the fraction tells you which root to take first, then the numerator tells you what power to raise it to.
  7. 0.5 · A negative exponent means flip to the reciprocal, then handle the fractional index as usual.
  8. 27 · Take the fourth root using the denominator, then raise that result to the third power from the numerator.
  9. 0.008 · Work the root and power first, then flip the result for the negative sign.
  10. 0.5 · Flip first to 1 over the square root of 4, which is 1/2 = 0.5.
Worksheet · LightMySky