How do you simplify (-64)^(-2/3)?

1 Answer
Mar 7, 2018

See a solution process below:

Explanation:

First, rewrite the expression as:

(-64)^(-2 xx 1/3)

Next, use this rule of exponents to separate the exponents:

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

(-64)^(color(red)(-2) xx color(blue)(1/3)) => (-64^color(red)(-2))^color(blue)(1/3)

Then, use this rule of exponents to eliminate the negative exponent:

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

(-64^color(red)(-2))^(1/3) => (1/-64^color(red)(- -2))^(1/3) => (1/-64^color(red)(2))^(1/3) =>

(1/4096)^(1/3) => 1/16