The expression $(a^5b^6)^4$ can be simplified using the power of a product property, which states $(xy)^n = x^n y^n$. You also apply the rule for exponents, $(x^m)^n = x^{m \cdot n}$.

Let's simplify step by step:

$(a^5b^6)^4 = (a^5)^4 \cdot (b^6)^4$

Now apply the exponent rule $(x^m)^n = x^{m \cdot n}$ to both terms:

$= a^{5 \cdot 4} \cdot b^{6 \cdot 4}$

$= a^{20} \cdot b^{24}$

Thus, the simplified expression is:

$a^{20}b^{24}$

Would you like more details or have any questions?

Here are 5 related questions to expand on this concept:

1. How would you simplify $(a^3b^2)^5$?
2. What is the result of $(x^4y^5)^3$?
3. How do you simplify $(a^2b^3c^4)^2$?
4. Can you explain the difference between $(ab)^n$ and $a^n \cdot b^n$?
5. How would you simplify $(a^7b^3)^6$?

Tip: When simplifying expressions with exponents, always apply the power rule carefully to both the base and its exponent!