Precalculus Examples

$\sqrt[3]{27 x^{- 6} y^{2}}$

Step 1

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

$\sqrt[3]{27 \frac{1}{x^{6}} y^{2}}$

Step 2

Combine exponents.

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Step 2.1

Combine $27$ and $\frac{1}{x^{6}}$ .

$\sqrt[3]{\frac{27}{x^{6}} y^{2}}$

Step 2.2

Combine $\frac{27}{x^{6}}$ and $y^{2}$ .

$\sqrt[3]{\frac{27 y^{2}}{x^{6}}}$

Step 3

Rewrite $\frac{27 y^{2}}{x^{6}}$ as ${(\frac{3}{x^{2}})}^{3} y^{2}$ .

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Step 3.1

Factor the perfect power $3^{3}$ out of $27 y^{2}$ .

$\sqrt[3]{\frac{3^{3} y^{2}}{x^{6}}}$

Step 3.2

Factor the perfect power ${(x^{2})}^{3}$ out of $x^{6}$ .

$\sqrt[3]{\frac{3^{3} y^{2}}{{(x^{2})}^{3} \cdot 1}}$

Step 3.3

Rearrange the fraction $\frac{3^{3} y^{2}}{{(x^{2})}^{3} \cdot 1}$ .

$\sqrt[3]{{(\frac{3}{x^{2}})}^{3} y^{2}}$

Step 4

Pull terms out from under the radical.

$\frac{3}{x^{2}} \sqrt[3]{y^{2}}$

Step 5

Combine $\frac{3}{x^{2}}$ and $\sqrt[3]{y^{2}}$ .

$\frac{3 \sqrt[3]{y^{2}}}{x^{2}}$