Question

How do you simplify `625^ { \frac { -1 } { 4} }`?

Answer 1

See a solution process below:

Explanation:

First, use this rule of exponents to rewrite the expression:

`x^color(red)(a) = 1/x^color(red)(-a)`

`625^color(red)(-1/4) = 1/625^color(red)(- -1/4) = 1/625^(1/4)`

We can now rewrite this as:

`1/(5^4)^(1/4) = 1/(5^(4 xx 1/4)) => 1/5^(4/4) => 1/5^1 => 1/5`