Simplify. Assume that all variables represent positive real numbers.
-$\sqrt[3]{32 x^{9} y^{7}}-\sqrt[3]{108 x^{12} y^{4}}$

A) $\left(2 x^{3} y^{2}-3 x^{4} y\right) \sqrt[3]{4 y}$
B) $\left(2 x^{3} y^{2}+3 x^{4} y\right) \sqrt[3]{4 y}$
C) $\left(2 x^{3} y^{2}+3 x^{4} y\right) \sqrt[3]{4}$
D) $\left(2 x^{6} y^{4}-3 x^{9} y\right) \sqrt[3]{4}$

Question

Simplify. Assume that all variables represent positive real numbers.
-$\sqrt[3]{32 x^{9} y^{7}}-\sqrt[3]{108 x^{12} y^{4}}$

A) $\left(2 x^{3} y^{2}-3 x^{4} y\right) \sqrt[3]{4 y}$
B) $\left(2 x^{3} y^{2}+3 x^{4} y\right) \sqrt[3]{4 y}$
C) $\left(2 x^{3} y^{2}+3 x^{4} y\right) \sqrt[3]{4}$
D) $\left(2 x^{6} y^{4}-3 x^{9} y\right) \sqrt[3]{4}$

Quizplus · Accepted Answer

First, simplify each term inside the cube roots: $\sqrt[3]{32 x^{9} y^{7}} = 2x^3y^{\frac{7}{3}}$ and $\sqrt[3]{108 x^{12} y^{4}} = 3x^4y^{\frac{4}{3}}$. Factoring out the common term $\sqrt[3]{4y}$ gives $(2 x^{3} y^{2}-3 x^{4} y) \sqrt[3]{4 y}$.

Simplify Assume That All Variables Represent Positive Real Numbers 32x9y73−108x12y43\sqrt[3]{32 x^{9} y^{7}}-\sqrt[3]{108 x^{12} y^{4}}332x9y7​−3108x12y4​

Simplify Assume That All Variables Represent Positive Real Numbers $\sqrt[3]{32 x^{9} y^{7}}-\sqrt[3]{108 x^{12} y^{4}}$