Question

How do you simplify `(5^sqrt2)^sqrt8`?

Answer 1

`(5^sqrt(2))^sqrt(8) = color(green)(625)`

Explanation:

For the general case
`color(white)("XXX")(x^a)^b= x^(ab)`

So
`color(white)("XXX")(5^sqrt(2))^sqrt(8) = 5^sqrt(16)=5^4=625`