Simplify 20x^6 cube root of -1/1000x^36

$20 x^{6} \sqrt[3]{\frac{- 1}{1000} x^{36}}$

Combine $\frac{- 1}{1000}$ and $x^{36}$ .

$20 x^{6} \sqrt[3]{\frac{- x^{36}}{1000}}$

Move the negative in front of the fraction.

$20 x^{6} \sqrt[3]{- \frac{x^{36}}{1000}}$

Rewrite $- \frac{x^{36}}{1000}$ as ${(- \frac{x^{12}}{10})}^{3}$ .

$20 x^{6} \sqrt[3]{{(- \frac{x^{12}}{10})}^{3}}$

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

$20 x^{6} (- \frac{x^{12}}{10})$

Cancel the common factor of $10$ .

Move the leading negative in $- \frac{x^{12}}{10}$ into the numerator.

$20 x^{6} \frac{- x^{12}}{10}$

Factor $10$ out of $20 x^{6}$ .

$10 (2 x^{6}) \frac{- x^{12}}{10}$

Cancel the common factor.

$10 (2 x^{6}) \frac{- x^{12}}{10}$

Rewrite the expression.

$2 x^{6} (- x^{12})$

Multiply $- 1$ by $2$ .

$- 2 x^{6} x^{12}$

Multiply $x^{6}$ by $x^{12}$ by adding the exponents.

Move $x^{12}$ .

$- 2 (x^{12} x^{6})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 2 x^{12 + 6}$

Add $12$ and $6$ .

$- 2 x^{18}$