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

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Answer 1 · 2018-03-07T08:23:30

See a solution process below:

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#