Alright, let's simplify the given expression step-by-step:
The given expression is:
[tex]\[ (6 n^{-5})(3 n^{-3})^2 \][/tex]
1. Simplify the part inside the parenthesis:
[tex]\[
(3 n^{-3})^2
\][/tex]
When raising a product to a power, raise both the constant and the variable:
[tex]\[
(3 n^{-3})^2 = 3^2 (n^{-3})^2 = 9 n^{-6}
\][/tex]
2. Now, substitute this back into the original expression:
[tex]\[
(6 n^{-5})(9 n^{-6})
\][/tex]
3. Multiply the constants:
[tex]\[
6 \cdot 9 = 54
\][/tex]
4. Combine the exponents for the same base [tex]\( n \)[/tex]:
[tex]\[
n^{-5} \cdot n^{-6} = n^{-5 + (-6)} = n^{-11}
\][/tex]
5. Combine the results:
[tex]\[
54 n^{-11}
\][/tex]
6. Rewriting [tex]\( n^{-11} \)[/tex] as a fraction:
[tex]\[
54 n^{-11} = \frac{54}{n^{11}}
\][/tex]
Thus, the equivalent expression is:
[tex]\[
\frac{54}{n^{11}}
\][/tex]
So, the correct answer is [tex]\( \text{D.} \frac{54}{n^{11}} \)[/tex].
