Question

How do you write the expression `(root4(5))^5` in exponential form?

Answer 1

See a solution process below:

Explanation:

First, use this rule for exponents to rewrite the radical:

`root(color(red)(n))(x) = x^(1/color(red)(n))`

`(root(color(red)(4))(5))^5 = (5^(1/color(red)(4)))^5`

Now, use this rule of exponents to combine the exponents:

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

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