Simplify the following radical expression. $\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }$
A) $4 p q \sqrt [ 3 ] { 6 p q ^ { 2 } }$
B) $4 p ^ { 3 } q ^ { 2 } \sqrt [ 3 ] { 6 q }$
C) $6 p q ^ { 2 } \sqrt [ 3 ] { 4 p q }$
D) $4 \sqrt [ 3 ] { 6 p q ^ { 2 } }$
E) $4 p ^ { 2 } q \sqrt [ 3 ] { 6 p q }$

Question

Quizplus · Accepted Answer

To simplify $\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }$, factor 384 into prime factors and express $p^4$ and $q^5$ in a way that some factors can be taken out of the cube root. $384 = 2^7 \cdot 3$, so $384 p^4 q^5 = 2^7 \cdot 3 p^4 q^5 = 2^6 \cdot 2 \cdot 3 p^3 \cdot p q^3 \cdot q^2$. Taking cube roots of perfect cubes out of the radical gives $4pq \sqrt[3]{6pq^2}$.

Simplify the Following Radical Expression 384p4q53\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }3384p4q5​

Simplify the Following Radical Expression $\sqrt [ 3 ] { 384 p ^ { 4 } q ^ { 5 } }$