To simplify the given expression step-by-step, follow these steps:
1. Simplify inside the parenthesis first:
[tex]\[
\left(\frac{-3 r^6 s^3}{r}\right)
\][/tex]
We can divide [tex]\(r^6\)[/tex] by [tex]\(r\)[/tex]:
[tex]\[
\frac{-3 r^6 s^3}{r} = -3 r^{6-1} s^3 = -3 r^5 s^3
\][/tex]
2. Now, take the simplified expression and square it:
[tex]\[
\left(-3 r^5 s^3\right)^2
\][/tex]
When squaring a product of terms, we square each term individually:
[tex]\[
\left(-3\right)^2 \left(r^5\right)^2 \left(s^3\right)^2
\][/tex]
3. Simplify each part separately:
[tex]\[
\left(-3\right)^2 = 9
\][/tex]
[tex]\[
\left(r^5\right)^2 = r^{5 \cdot 2} = r^{10}
\][/tex]
[tex]\[
\left(s^3\right)^2 = s^{3 \cdot 2} = s^6
\][/tex]
4. Combine all the simplified parts together:
[tex]\[
9 r^{10} s^6
\][/tex]
So, the simplified expression is:
[tex]\[
9 r^{10} s^6
\][/tex]
Therefore, the correct answer is:
[tex]\[
9 r^{10} s^6
\][/tex]
