which of the following is equivalent to $left(16^{\frac{3}{2}}\right)^{\frac{1}{2}}$?\n6\n8\n12\n64

Answer:

B. 8

Explanation:

Step1: Simplify the inner - exponent

First, find $16^{\frac{3}{2}}$. We know that $a^{\frac{m}{n}}=\sqrt[n]{a^{m}}$. So, $16^{\frac{3}{2}}=\sqrt{16^{3}}$. Since $16 = 4^{2}$, then $16^{3}=(4^{2})^{3}=4^{6}$ by the power - of - a - power rule $(a^{m})^{n}=a^{mn}$. And $\sqrt{16^{3}}=\sqrt{4^{6}} = 4^{3}=64$.

Step2: Simplify the outer - exponent

Now we have $(16^{\frac{3}{2}})^{\frac{1}{2}}$, and since we found $16^{\frac{3}{2}} = 64$, then $(16^{\frac{3}{2}})^{\frac{1}{2}}=64^{\frac{1}{2}}$. Using the rule $a^{\frac{1}{n}}=\sqrt[n]{a}$, we get $64^{\frac{1}{2}}=\sqrt{64}=8$.