Simplify.
-$\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 7 } }$
A) $4 a ^ { 2 } b \sqrt [ 3 ] { a ^ { 4 } b ^ { 2 } }$
B) $- 4 a ^ { 4 } b ^ { 2 } \sqrt [ 3 ] { a ^ { 2 } b }$
C) $4 \sqrt { a ^ { 7 } b ^ { 14 } }$
D) $4 a b \sqrt [ 3 ] { a ^ { 3 } b ^ { 5 } }$

Question

Quizplus · Accepted Answer

The cube root of $-64$ is $-4$, and for the variables, we use the property that $\sqrt[3]{x^3} = x$ for any real number $x$. For $a^{14}$, we can rewrite it as $a^{4 \cdot 3 + 2} = a^{12}a^{2}$, and for $b^{7}$, we can rewrite it as $b^{2 \cdot 3 + 1} = b^{6}b$. Thus, the cube root simplifies to $-4a^{4}b^{2}\sqrt[3]{a^{2}b}$.

Simplify - −64a14b73\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 7 } }3−64a14b7​

Simplify
- $\sqrt [ 3 ] { - 64 a ^ { 14 } b ^ { 7 } }$