To simplify the expression [tex]\(\sqrt{16 r^6}\)[/tex], let's break it down step-by-step:
1. Identify the expression under the square root:
[tex]\[
\sqrt{16 r^6}
\][/tex]
2. Rewrite the expression under the square root:
[tex]\[
16 r^6 = (4^2) (r^6)
\][/tex]
3. Use the property of square roots that [tex]\(\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}\)[/tex]:
[tex]\[
\sqrt{16 r^6} = \sqrt{16} \cdot \sqrt{r^6}
\][/tex]
4. Evaluate the square root of 16:
[tex]\[
\sqrt{16} = 4
\][/tex]
5. Evaluate the square root of [tex]\(r^6\)[/tex]. Recall that [tex]\(\sqrt{r^6} = r^{6/2}\)[/tex]:
[tex]\[
\sqrt{r^6} = r^3
\][/tex]
6. Combine the results from steps 4 and 5:
[tex]\[
\sqrt{16 r^6} = 4 \cdot r^3
\][/tex]
Thus, the simplified expression is:
[tex]\[
4 r^3
\][/tex]
Therefore, the correct answer is:
[tex]\[
4 r^3
\][/tex]
