Question

How do you simplify `125^(2/3)`?

Answer 1

`=color(blue)(25`

Explanation:

`125^(2/3`

`125 = 5 xx 5 xx 5`

`125 = 5 ^3`

`125^(2/3) = 5^(3 (2/3)`

...................................................................................
Consider just the indices:
`3xx2/3 = (cancel(3)^1xx2)/(cancel(3)^1) = 2`
..............................................................................

`= 5^2`

`=color(blue)(25`

Answer 2

`color(red)25`

Explanation:

`125^(2/3)`

`:.=root3(125^2)`

`:.=root3(15625)`

`:.=root3(25*25*25)`

`:.color(red)(=root3(a) xx root3(a) xx root3(a)=a`

`:.color(red)(=25`