Algebra Examples

${(\frac{1}{32})}^{- \frac{2}{5}}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

$32^{\frac{2}{5}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $32$ as $2^{5}$ .

${(2^{5})}^{\frac{2}{5}}$

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$2^{5 (\frac{2}{5})}$

Step 3

Cancel the common factor of $5$ .

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Step 3.1

Cancel the common factor.

$2^{5 (\frac{2}{5})}$

Step 3.2

Rewrite the expression.

$2^{2}$

Step 4

Raise $2$ to the power of $2$ .

$4$