Precalculus Examples

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

Step 1

Reduce the expression $\frac{27^{- \frac{2}{3}}}{27^{- \frac{1}{3}}}$ by cancelling the common factors.

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Step 1.1

Factor $27^{- \frac{1}{3}}$ out of $27^{- \frac{2}{3}}$ .

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

Step 1.2

Multiply by $1$ .

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

Step 1.3

Cancel the common factor.

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

Step 1.4

Rewrite the expression.

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

Step 2

Divide $27^{- \frac{1}{3}}$ by $1$ .

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

Step 3

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

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

Step 4

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\frac{1}{\sqrt[3]{27^{1}}}$

Step 5

Anything raised to $1$ is the base itself.

$\frac{1}{\sqrt[3]{27}}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{\sqrt[3]{27}}$

Decimal Form:

$0.\overline{3}$