Simplify. Assume that all variables represent positive real numbers.
-$$\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 10 } }$$
A) $ 4 \sqrt{\mathrm{a}^{10} \mathrm{~b}^{14}} $
B) $ 4 a^{2} b \sqrt[3]{a^{4} b^{3}} $
C) $ -4 a^{4} b^{3} \sqrt[3]{a^{2} b} $
D) $ 4 a b \sqrt[3]{a^{4} b^{5}} $

Question

Quizplus · Accepted Answer

The cube root of $-64$ is $-4$, and for the variables, we divide the exponents by 3, keeping in mind that the result should be in the simplest form for a cube root. This gives us $a^{14/3}$ and $b^{10/3}$, which simplifies to $-4 a^{4} b^{3} \sqrt[3]{a^{2} b}$, matching option C.

Simplify Assume That All Variables Represent Positive Real Numbers −64a14b103\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 10 } }3−64a14b10​

Simplify Assume That All Variables Represent Positive Real Numbers $\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 10 } }$