Simplify the radical. Assume that all variables represent positive real numbers.
-$9 \sqrt [ 3 ] { \frac { c ^ { 18 } d ^ { 20 } } { 64 } }$
A) $\frac { 27 } { 64 } c ^ { 18 } d ^ { 20 } \sqrt [ 3 ] { c d }$
B) $\frac { 9 } { 4 } c d \sqrt [ 3 ] { c ^ { 18 } d ^ { 20 } }$
C) $\frac { 9 } { 4 } c ^ { 6 } d ^ { 6 } \sqrt [ 3 ] { d ^ { 2 } }$
D) $\frac { 9 } { 64 } c ^ { 6 } d ^ { 7 }$

Question

Quizplus · Accepted Answer

To simplify $9 \sqrt [ 3 ] { \frac { c ^ { 18 } d ^ { 20 } } { 64 } }$, we first simplify inside the radical. The cube root of $c^{18}$ is $c^6$ because $18/3=6$, the cube root of $d^{20}$ is $d^6$ times $\sqrt[3]{d^2}$ because $20/3=6$ remainder 2, and the cube root of $64$ is $4$ because $64=4^3$. Thus, the expression simplifies to $\frac{9}{4}c^6d^6\sqrt[3]{d^2}$.

Simplify the Radical 9c18d206439 \sqrt [ 3 ] { \frac { c ^ { 18 } d ^ { 20 } } { 64 } }9364c18d20​​

Simplify the Radical $9 \sqrt [ 3 ] { \frac { c ^ { 18 } d ^ { 20 } } { 64 } }$