which of the following is equivalent to $left(16^{\frac{3}{2}}\right)^{\frac{1}{2}}$?\no 6\no 8\no 12\no 64

Explanation:

Step1: Simplify the inner - exponent

First, calculate $16^{\frac{3}{2}}$. We know that $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. So, $16^{\frac{3}{2}}=\sqrt{16^{3}}$. Since $\sqrt{16} = 4$, then $16^{\frac{3}{2}}=(\sqrt{16})^{3}=4^{3}=64$.

Step2: Calculate the outer - exponent

Now we have $(16^{\frac{3}{2}})^{\frac{1}{2}}$, which is $64^{\frac{1}{2}}$ after the first step. And $64^{\frac{1}{2}}=\sqrt{64}=8$.

Answer:

8