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Simplify - fourth root of 81/(x^12)

$- \sqrt[4]{\frac{81}{x^{12}}}$

Step 1

Rewrite $81$ as $3^{4}$ .

$- \sqrt[4]{\frac{3^{4}}{x^{12}}}$

Step 2

Rewrite $x^{12}$ as ${(x^{3})}^{4}$ .

$- \sqrt[4]{\frac{3^{4}}{{(x^{3})}^{4}}}$

Step 3

Rewrite $\frac{3^{4}}{{(x^{3})}^{4}}$ as ${(\frac{3}{x^{3}})}^{4}$ .

$- \sqrt[4]{{(\frac{3}{x^{3}})}^{4}}$

Step 4

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

$- \frac{3}{x^{3}}$

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