Question

simplify. assume that all variables are positive.
\\(\sqrt3{- 128x^{6}y^{5}}\\)
\\(\sqrt3{- 128x^{6}y^{5}} = \square\\)
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Factor out perfect cubes

$\sqrt[3]{-128x^6y^5} = \sqrt[3]{-64 \cdot 2 \cdot x^6 \cdot y^3 \cdot y^2}$

Step2: Separate perfect cube factors

$\sqrt[3]{-64} \cdot \sqrt[3]{x^6} \cdot \sqrt[3]{y^3} \cdot \sqrt[3]{2y^2}$

Step3: Simplify perfect cube roots

$-4 \cdot x^2 \cdot y \cdot \sqrt[3]{2y^2}$

Step4: Combine terms

$-4x^2y\sqrt[3]{2y^2}$

Answer:

$-4x^2y\sqrt[3]{2y^2}$