The problem asks to find which exponential expression is equal to $(6^{-3})^6$.

Let's simplify $(6^{-3})^6$:

1. Using the power of a power rule in exponents, $(a^m)^n = a^{m \cdot n}$, we multiply the exponents.

   $(6^{-3})^6 = 6^{-3 \cdot 6} = 6^{-18}$

Now, we can look at the answer choices:

• A: $\frac{6^3}{6^6}$

  Applying the quotient rule for exponents $\frac{a^m}{a^n} = a^{m-n}$:

  $\frac{6^3}{6^6} = 6^{3-6} = 6^{-3}$

  This does not match $6^{-18}$.

• B: $(6^4)^{11}$

  Apply the power of a power rule:

  $(6^4)^{11} = 6^{4 \cdot 11} = 6^{44}$

  This does not match $6^{-18}$.

• C: $\frac{6^{-3}}{6^{15}}$

  Again, apply the quotient rule:

  $\frac{6^{-3}}{6^{15}} = 6^{-3 - 15} = 6^{-18}$

  This matches $6^{-18}$.

• D: $(6^4)^{-5}$

  Apply the power of a power rule:

  $(6^4)^{-5} = 6^{4 \cdot (-5)} = 6^{-20}$

  This does not match $6^{-18}$.

Thus, the correct answer is C: $\frac{6^{-3}}{6^{15}}$.

Would you like more details or explanations on any part of the process? Here are 5 related questions to practice further:

1. Simplify $(4^{-2})^5$.
2. What is the simplified form of $\frac{7^5}{7^{12}}$?
3. Simplify the expression $(2^3)^4 \times 2^{-6}$.
4. Evaluate $(8^{-1})^3$.
5. Simplify $\frac{10^{-4}}{10^{-9}}$.

Tip: When simplifying exponents, always remember to apply the rules for powers and quotients carefully to avoid mistakes!