Algebra Examples

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

Step 1

Multiply the exponents in ${(27^{- \frac{1}{3}})}^{2}$ .

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Step 1.1

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

$27^{- \frac{1}{3} \cdot 2}$

Step 1.2

Multiply $- \frac{1}{3} \cdot 2$ .

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Step 1.2.1

Multiply $2$ by $- 1$ .

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

Step 1.2.2

Combine $- 2$ and $\frac{1}{3}$ .

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

Step 1.3

Move the negative in front of the fraction.

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

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{27^{\frac{2}{3}}}$

Step 3

Simplify the denominator.

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Step 3.1

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

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

Step 3.2

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

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

Step 3.3

Cancel the common factor of $3$ .

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Step 3.3.1

Cancel the common factor.

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

Step 3.3.2

Rewrite the expression.

$\frac{1}{3^{2}}$

Step 3.4

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

$\frac{1}{9}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$