Use the product rule to multiply. Assume all variables represent positive real numbers.
-$\sqrt [ 5 ] { 5 x ^ { 4 } } \cdot \sqrt [ 5 ] { 81 }$
A) $405 x ^ { 4 }$
B) $9 x ^ { 2 }$
C) $\sqrt { 405 x ^ { 4 } }$
D) $\sqrt [ 5 ] { 405 x ^ { 4 } }$

Question

Quizplus · Accepted Answer

The product rule for radicals allows you to multiply the radicands (the numbers under the radical) when the indices (the small number outside the radical) are the same. Here, both radicals have an index of 5, so you multiply the radicands: $5x^4 \cdot 81 = 405x^4$. Thus, the answer is $\sqrt[5]{405x^4}$.

Use the Product Rule to Multiply 5x45⋅815\sqrt [ 5 ] { 5 x ^ { 4 } } \cdot \sqrt [ 5 ] { 81 }55x4​⋅581​

Use the Product Rule to Multiply $\sqrt [ 5 ] { 5 x ^ { 4 } } \cdot \sqrt [ 5 ] { 81 }$