Algebra Examples

${(\frac{1}{27})}^{- \frac{2}{3}}$

Step 1

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

$27^{\frac{2}{3}}$

Step 2

Simplify the expression.

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Step 2.1

Rewrite $27$ as $3^{3}$ .

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

Step 2.2

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

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

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Cancel the common factor.

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

Step 3.2

Rewrite the expression.

$3^{2}$

Step 4

Raise $3$ to the power of $2$ .

$9$