Question

simplify, if possible. (if not possible, enter impossible.)
\sqrt3{\frac{-16}{27}}

Explanation:

Step1: Split cube root into parts

$$\sqrt[3]{\frac{-16}{27}} = \frac{\sqrt[3]{-16}}{\sqrt[3]{27}}$$

Step2: Simplify denominator cube root

$\sqrt[3]{27} = 3$, since $3^3=27$

Step3: Factor numerator radical

$$\sqrt[3]{-16} = \sqrt[3]{-8 \times 2} = \sqrt[3]{-8} \times \sqrt[3]{2} = -2\sqrt[3]{2}$$

Step4: Combine simplified terms

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

Answer:

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