Trigonometry Examples

$\sqrt[3]{27^{- 2}}$

Step 1

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

$\sqrt[3]{\frac{1}{27^{2}}}$

Step 2

Raise $27$ to the power of $2$ .

$\sqrt[3]{\frac{1}{729}}$

Step 3

Rewrite $\sqrt[3]{\frac{1}{729}}$ as $\frac{\sqrt[3]{1}}{\sqrt[3]{729}}$ .

$\frac{\sqrt[3]{1}}{\sqrt[3]{729}}$

Step 4

Any root of $1$ is $1$ .

$\frac{1}{\sqrt[3]{729}}$

Step 5

Simplify the denominator.

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Step 5.1

Rewrite $729$ as $9^{3}$ .

$\frac{1}{\sqrt[3]{9^{3}}}$

Step 5.2

Pull terms out from under the radical, assuming real numbers.

$\frac{1}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{9}$

Decimal Form:

$0.\overline{1}$