How do you simplify ${(- 32)}^{- \frac{3}{5}}$ $(-32)^(-3/5)$ ?

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Answer 1 · 2016-10-13T14:45:15

$= \frac{1}{- 8}$ $= 1/(-8)$

There are two laws of indices in place here.

$x^{- m} = \frac{1}{x^{m}} and x^{\frac{p}{q}} = {(\sqrt[q]{x})}^{p}$ $x^-m = 1/x^m" and "x^(p/q) = (rootq(x))^p$

Use the sign law first to make the index positive.

$\frac{1}{{(- 32)}^{\frac{3}{5}}}$ $1/((-32)^(3/5)$

Change the index to a root and a power:

$= \frac{1}{{\sqrt[5]{(- 32)}}^{3}} \leftarrow$ $=1/color(red)(root5((-32)))^(3)" "larr$ find 5th root of -32

$= \frac{1}{{(- 2)}^{3}} \leftarrow$ $= 1/((-2)^3)" "larr$ find the cube of -2

$= \frac{1}{- 8}$ $= 1/(-8)$

How do you simplify (-32)^(-3/5)(−32)−35(-32)^(-3/5)?