Question

How do you evaluate `(5^ { 8} ) ^ { \frac { 1} { 2} }`?

Answer 1

See a solution process below:

Explanation:

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

`(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`

`(5^color(red)(8))^color(blue)(1/2) => 5^(color(red)(8) xx color(blue)(1/2)) => 5^4`

We can now evaluate this as:

`5^4 => 5 xx 5 xx 5 xx 5 => 25 xx 5 xx 5 => 125 xx 5 =>`

`625`