Simplify cube root of 1/1000c^9d^12

$\sqrt[3]{\frac{1}{1000} c^{9} d^{12}}$

Combine $\frac{1}{1000}$ and $c^{9}$ .

$\sqrt[3]{\frac{c^{9}}{1000} d^{12}}$

Combine $\frac{c^{9}}{1000}$ and $d^{12}$ .

$\sqrt[3]{\frac{c^{9} d^{12}}{1000}}$

Rewrite $c^{9} d^{12}$ as ${(c^{3} d^{4})}^{3}$ .

$\sqrt[3]{\frac{{(c^{3} d^{4})}^{3}}{1000}}$

Rewrite $1000$ as $10^{3}$ .

$\sqrt[3]{\frac{{(c^{3} d^{4})}^{3}}{10^{3}}}$

Rewrite $\frac{{(c^{3} d^{4})}^{3}}{10^{3}}$ as ${(\frac{c^{3} d^{4}}{10})}^{3}$ .

$\sqrt[3]{{(\frac{c^{3} d^{4}}{10})}^{3}}$

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

$\frac{c^{3} d^{4}}{10}$