The expression $(x^3)^2(y^2)^4$ can be simplified by using the power of a power rule, which states:

$(a^m)^n = a^{m \cdot n}$

Let's apply this rule to each part:

1. $(x^3)^2 = x^{3 \cdot 2} = x^6$
2. $(y^2)^4 = y^{2 \cdot 4} = y^8$

Now, multiply the two simplified expressions together:

$x^6 y^8$

Thus, $(x^3)^2(y^2)^4 = x^6 y^8$.

Would you like further details or have any questions?

Here are 5 related questions:

1. How do you simplify $(x^5)^3(y^4)^2$?
2. What is the rule for multiplying powers with the same base?
3. How would you simplify $(xy^2)^3$?
4. What is the expanded form of $(x^4)^3 (y^3)^2$?
5. Can you explain the difference between the power of a power rule and the product of powers rule?

Tip: When working with exponents, always remember to handle each base separately before combining terms.