Simplify the expression. Assume the letters denote any real numbers. $\sqrt [ 5 ] { a ^ { 3 } b } \cdot \sqrt [ 5 ] { a ^ { 7 } b }$
A) $b ^ { 5 } \sqrt [ 5 ] { a ^ { 2 } }$
B) $a ^ { 2 } \sqrt [ 5 ] { b }$
C) $a ^ { 5 } \sqrt { b ^ { 2 } }$
D) $a ^ { 2 } \sqrt [ 5 ] { b ^ { 2 } }$
E) $a ^ { 2 } b ^ { 2 } \sqrt { 5 }$

Question

Quizplus · Accepted Answer

Using the product property of radicals, we have:
\begin{align*}
\sqrt [ 5 ] { a ^ { 3 } b } \cdot \sqrt [ 5 ] { a ^ { 7 } b } &= \sqrt [ 5 ] {a^3ba^7b} \
&= \sqrt [ 5 ] {a^{10}b^2} \
&= \sqrt [ 5 ] {a^2 \cdot (a^5)^2 \cdot b^2} \
&= a^2 \sqrt [ 5 ] {b^2}.
\end{align*}Therefore, the answer is D.

Simplify the Expression a3b5⋅a7b5\sqrt [ 5 ] { a ^ { 3 } b } \cdot \sqrt [ 5 ] { a ^ { 7 } b }5a3b​⋅5a7b​

Simplify the Expression $\sqrt [ 5 ] { a ^ { 3 } b } \cdot \sqrt [ 5 ] { a ^ { 7 } b }$