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Write as a single power, then evaluate:?  (-32)^3/5 * (-32)^-4/5 / (-32)^2/5  

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dstrong777 | eNotes Newbie

Posted May 25, 2013 at 8:21 PM via web

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Write as a single power, then evaluate:?

 (-32)^3/5 * (-32)^-4/5 / (-32)^2/5

 

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted May 25, 2013 at 8:53 PM (Answer #1)

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`[(-32)^(3/5) xx (-32)^(-4/5)]/(-32)^(2/5)`

We know that `(x^a)^(b) = x^(ab)`

`(-32)^3/5 = ((-2)^5)^(3/5) = (-2)^3 = -8`

`(-32)^-4/5 = ((-2)^5)^(-4/5) = (-2)^-4 = 1/16`

`(-32)^2/5 = ((-2)^5)^(2/5) = (-2)^2 = 4`

 

 

` [(-32)^(3/5)xx(-32)^(-4/5)]/(-32)^(2/5)`

 

`= (-8)/(4xx16)`

`= -1/8`

 

So the answer is -1/8.

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