Question

How do you simplify `(a^(4/5) * c^(-1/3))^5`?

Answer 1

See the entire simplification process below:

Explanation:

First, apply this rule for exponents:

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

`(a^color(red)(4/5) * c^color(red)(-1/3))^color(blue)(5)-> a^(color(red)(4/5) xx color(blue)(5)) * c^(color(red)(-1/3) xx color(blue)(5)) -> a^4 * c^(-5/3)`

If we want to have this simplified having no negative exponents we can use this rule for exponents:

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

`a^4 * c^color(red)(-5/3) -> a^4/c^(- color(red)(-5/3)) -> a^4/c^ color(red)(5/3)`