The expression $(X^4)^5$ simplifies by applying the power of a power rule. This rule states that when raising a power to another power, you multiply the exponents. So:

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

Thus, the simplified expression is:

$X^{20}$

Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would you simplify $(X^3)^6$?
2. What is $(Y^5)^3$?
3. How does the power rule apply to $(2X^2)^4$?
4. Can you simplify the expression $(X^4 Y^3)^2$?
5. What happens if you raise a power of zero, like $(X^0)^5$?

Tip: When raising a product or quotient to a power, distribute the exponent to each factor in the product or quotient.