what is the square root of $r^{64}$?\n$r^{4}$\n$r^{8}$\n$r^{16}$\n$r^{32}$

Explanation:

Step1: Recall square - root rule

The square root of a number $x$ can be written as $x^{\frac{1}{2}}$. So, $\sqrt{r^{64}}=(r^{64})^{\frac{1}{2}}$.

Step2: Apply power - of - a - power rule

According to the power - of - a - power rule $(a^{m})^{n}=a^{mn}$. Here, $a = r$, $m = 64$, and $n=\frac{1}{2}$. Then $(r^{64})^{\frac{1}{2}}=r^{64\times\frac{1}{2}}$.

Step3: Calculate the exponent

$64\times\frac{1}{2}=32$, so $r^{64\times\frac{1}{2}}=r^{32}$.

Answer:

D. $r^{32}$