Algebra Examples

$(\frac{1}{216^{- \frac{2}{3}}})$

Step 1

Simplify the expression.

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Step 1.1

Move $216^{- \frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$216^{\frac{2}{3}}$

Step 1.2

Rewrite $216$ as $6^{3}$ .

${(6^{3})}^{\frac{2}{3}}$

Step 1.3

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

$6^{3 (\frac{2}{3})}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$6^{3 (\frac{2}{3})}$

Step 2.2

Rewrite the expression.

$6^{2}$

Step 3

Raise $6$ to the power of $2$ .

$36$