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Year 10 · Place Value

Fractional and negative indices

A fractional index is a root, and a negative index is a reciprocal.

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How to do it

  1. a^(1/2) is the square root, a^(1/3) the cube root.
  2. a^(m/n): take the nth root, then the mth power.
  3. a^(−n) = 1 ÷ aⁿ.

Worked example

64^(1/3) = ?
A power of 1/3 means the cube root: ∛64 = 4.
Answer: 4

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Root first, then power, keeps the numbers small.

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