Simplify cube root of -54* cube root of 1/2

$\sqrt[3]{- 54} \cdot \sqrt[3]{\frac{1}{2}}$

Combine using the product rule for radicals.

$\sqrt[3]{- 54 \cdot \frac{1}{2}}$

Combine $- 54$ and $\frac{1}{2}$ .

$\sqrt[3]{\frac{- 54}{2}}$

Simplify the expression.

Divide $- 54$ by $2$ .

$\sqrt[3]{- 27}$

Rewrite $- 27$ as ${(- 3)}^{3}$ .

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

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

$- 3$