Simplify cube root of square root of 729/(x^6)

$\sqrt[3]{\sqrt{\frac{729}{x^{6}}}}$

Step 1

Rewrite $729$ as $27^{2}$ .

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

Step 2

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

$\sqrt[3]{\sqrt{\frac{27^{2}}{{(x^{3})}^{2}}}}$

Step 3

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

$\sqrt[3]{\sqrt{{(\frac{27}{x^{3}})}^{2}}}$

Step 4

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

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

Step 5

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

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

Step 6

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

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

Step 7

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

$\frac{3}{x}$