Question

How do you simplify `(1/27)^(-2/3)`?

Answer 1

See a solution process below:

Explanation:

Using these rules for exponents we can rewrite the expression as:

• `(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))`
• `1/x^color(red)(a) = x^color(red)(-a)`

`(1/27)^(color(red)(1/3) xx color(blue)(-2) =>`

`((1/27)^(color(red)(1/3)))^color(blue)(-2) =>`

`(1^color(red)(1/3)/27^color(red)(1/3))^color(blue)(-2) =>`

`(1/3)^color(blue)(-2) =>`

`1^color(blue)(-2)/3^color(blue)(-2) =>`

`1/3^color(blue)(-2) =>`

`3^color(blue)(- -2) =>`

`3^color(blue)(2) =>`

`9`