Question

How do you write with fractional exponents `1/5(sqrt x^2)`?

Answer 1

`color(red)( 1/5 (sqrtx)^2 = 1/5x)`

Explanation:

`1/5 (sqrtx)^2 = 1/5 (x^(1/2))^2`

But `(x^a)^b = x^(ab)`, so

`(x^(1/2))^2= x^(2/2) =x^1 = x`

∴ `1/5 (sqrtx)^2 = 1/5x`