Question

\\\sqrt3{16x^9z^5}\\

assume that all of the variables in the expression represent positive real numbers.

Explanation:

Factor the radicand into perfect cubes

$$ 16x^9z^5 = (8 \cdot 2) \cdot (x^9) \cdot (z^3 \cdot z^2) = (2^3 \cdot x^9 \cdot z^3) \cdot (2z^2) $$

Apply the product rule for radicals

$$ \sqrt[3]{16x^9z^5} = \sqrt[3]{2^3 \cdot x^9 \cdot z^3} \cdot \sqrt[3]{2z^2} $$

Simplify the perfect cube factors

$$ \sqrt[3]{2^3 \cdot x^9 \cdot z^3} \cdot \sqrt[3]{2z^2} = 2x^3z\sqrt[3]{2z^2} $$

Answer:

\(\sqrt[3]{16x^9z^5} =\) <blank>\(2x^3z\sqrt[3]{2z^2}\)</blank>