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

Taming zero and negative powers

Mathematics · Number Representation & Place Value · ages 14-15
Name ______________________   Date ____________

  1. Work out 7⁰.

    Answer: ______________

  2. Which of these means the same thing as x⁻³?

    • 1/x³
    • x³
    • -3x
    • -x³

  3. True or false: x⁰ = 1 for any nonzero value of x.

    Circle one:   True   False

  4. Work out 5 to the minus 2 as a decimal.

    Answer: ______________

  5. Rewrite y⁻⁵ ÷ y⁻² with a positive index.

    • 1/y³
    • y³
    • 1/y⁷
    • y⁷

  6. x⁵ ÷ x⁵ is a number divided by itself. Using the quotient rule, this also equals x^(5-5) = x⁰. What must x⁰ equal?

    • 1
    • 0
    • x
    • 5

  7. Simplify 2x⁻⁴ · 3x⁶, writing your answer with a positive index.

    • 6x²
    • 6x⁻²
    • 6x¹⁰
    • x²/6

  8. Work out 2 to the minus 3 as a decimal.

    Answer: ______________

  9. Simplify (2 a to the minus 3) squared, giving a positive index.

    • 4 over a to the 6th
    • 4 a to the 6th
    • 2 over a to the 6th

  10. Simplify (x² · x⁻⁵) ÷ x⁻⁴.

    • x
    • x⁻¹
    • x⁷
    • 1/x⁷
LightMySky · lightmysky.comW1-mt_jAtXBSVqkj-s1

Answer key

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

Taming zero and negative powers W1-mt_jAtXBSVqkj-s1

  1. 1 · Any nonzero number raised to the power 0 is 1.
  2. 1/x³ · A negative index tells you to flip the base into a fraction and drop the minus sign.
  3. True · Any nonzero number divided by itself equals 1, and the quotient rule shows that division also equals x to the power 0.
  4. 0.04 · 5 to the minus 2 means 1 over 25, which is 0.04.
  5. 1/y³ · Subtract the indices for a division, then flip a negative result into a fraction.
  6. 1 · Two ways of writing the same division must give the same answer.
  7. 6x² · Multiply the coefficients and add the indices, since it's the same base being multiplied.
  8. 0.125 · 2 to the minus 3 means 1 over 8, which is 0.125.
  9. 4 over a to the 6th · Square each factor, then flip the negative index into a fraction.
  10. x · Combine the multiplication first, then the division, adding and subtracting indices as you go.
Worksheet · LightMySky