Question

How do you simplify `(27p^6)^(5/3)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`(3^3p^6)^(5/3)`

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

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

`(3^color(red)(3)p^color(red)(6))^color(blue)(5/3) => 3^(color(red)(3) xx color(blue)(5/3))9^(color(red)(6) xx color(blue)(5/3)) => 3^(15/3)p^(30/3) => 3^5p^10 =>`

`243p^10`