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.

Learn how to simplify the expression (X⁴)⁵ by applying the power of a power rule, which states that you multiply the exponents. The solution involves multiplying 4 and 5 to get X²⁰. This concept is essential for algebra and exponents, suitable for students in Grades 8-10.

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