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