Use the product rule to multiply. Assume all variables represent positive real numbers.
-$$\sqrt [ 4 ] { 16 } \cdot \sqrt [ 4 ] { 256 n ^ { 4 } }$$
A) $6 n$
B) $- 2 n$
C) $- 8 n$
D) $8 n$

Question

Quizplus · Accepted Answer

The product rule for radicals states that $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$. Applying this rule, we have $\sqrt[4]{16} \cdot \sqrt[4]{256n^4} = \sqrt[4]{16 \cdot 256n^4}$. Simplifying inside the radical, $16 = 2^4$ and $256 = 2^8$, so $16 \cdot 256n^4 = 2^4 \cdot 2^8n^4 = 2^{12}n^4$. Since $2^{12} = (2^3)^4 = 8^4$ and $n^4$ is already in the correct form for a fourth root, we have $\sqrt[4]{8^4n^4} = 8n$.

Use the Product Rule to Multiply 164⋅256n44\sqrt [ 4 ] { 16 } \cdot \sqrt [ 4 ] { 256 n ^ { 4 } }416​⋅4256n4​

Use the Product Rule to Multiply $\sqrt [ 4 ] { 16 } \cdot \sqrt [ 4 ] { 256 n ^ { 4 } }$