GCSE(F), GCSE(H),

When calculating with indices, roots may be shown as a fraction.

For example, `4^[1/2]` is the same as √4. A cube root of 4 is shown as `4^frac(1)(3)` .

1. Calculate `125^frac(1)(3) xx 5^2`. Give your answer without a power.

Answer: 125

`125^frac(1)(3) xx 5^2`

`root(3)125 xx 5^2`

`5 xx 25`

= 125

2. Show that `81^frac(1)(4) xx 9^frac(1)(2) = 9`.

Answer: `81^frac(1)(4) xx 9^frac(1)(2) = 9`

`root(4)81 xx root(2)9 = 9`

`3 xx 3 = 9`

Show all the steps; just showing an answer may lose marks.

Our iOS app has over 1,000 questions to help you practice this and many other topics.

Available to download free on the App Store.

Available to download free on the App Store.