How do you simplify #(- \frac { 27} { 125} ) ^ { - 2/ 3}#?

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Answer 1 · 2016-11-28T18:55:49

#25/9#

There are 2 negative signs, they mean very different things.

The negative sign inside the bracket refers to a negative number on the number line, to the left of 0.

the negative in the index indicates that the fraction inside the bracket has been inverted.
Recall: #x^-m = 1/x^m#

Get rid of the negative in the index first by finding the reciprocal of the fraction. It is still negative.

#(-27/125)^(-2/3) = (-125/27)^(2/3)#

Recall: #x^(p/q) = rootq (x^p) = (rootq x)^p#

#(-125/27)^(2/3) = (root 3 (-125/27))^2" "larr# both are cubes

=#(-5/3)^2#

=#25/9#