Multiply the radicals with different indices. Write the answer in radical form and simplify. $$\sqrt [ 3 ] { x y } \cdot \sqrt [ 5 ] { x y }$$
A) $\sqrt [ 15 ] { x ^ { 2 } y ^ { 2 } }$
B) $\sqrt [ 8 ] { x y }$
C) $\sqrt [ 15 ] { ( x y ) ^ { 8 } }$
D) $\sqrt [ 15 ] { x y }$

Question

Quizplus · Accepted Answer

To multiply radicals with different indices, convert them to exponential form: $ (xy)^{1/3} \cdot (xy)^{1/5} = (xy)^{1/3 + 1/5} = (xy)^{8/15} $. Convert back to radical form: $\sqrt[15]{(xy)^8}$.

Multiply the Radicals with Different Indices xy3⋅xy5\sqrt [ 3 ] { x y } \cdot \sqrt [ 5 ] { x y }3xy​⋅5xy​

Multiply the Radicals with Different Indices $\sqrt [ 3 ] { x y } \cdot \sqrt [ 5 ] { x y }$