Calculating with Fractional Indices

# Calculating with Fractional Indices

GCSE(H),

For a fractional index, the numerator is a power term, and the denominator is a root term.

27^frac(2)(3) means square 27 then cube root the answer; or cube root 27 then square the answer. Choose the easiest calculation. In this instance, the cube root of 27 is 3, and 3 squared is 9.

## Examples

1. Simplify sqrt(2) xx root(4)2, and show with a fractional index.

Answer: 2^frac(3)(4)

sqrt(2) xx root(4)2

= 2^frac(1)(2) xx 2^frac(1)(4)

= 2^frac(3)(4)

2. Simplify √5 ÷ 25. Leave the index as a fraction.

Answer: 5^(frac(-3)(2)

sqrt(5) ÷ 25

5^frac(1)(2) ÷ 5^2

5^(frac(1)(2) - 2)

5^-frac(3)(2)