If an index is a fraction, it is actually a root.

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

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

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

`root(3)125 xx 5^2`

`5 xx 25`

= 125

Answer: 125

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

Show all the steps to get the marks.

Answer:

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

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

`3 xx 3 = 9`

See also Integer Powers and Roots

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