To simplify the expression \( (-2p^4)^5 \), apply the power of a product rule, which states:

\[
(a \cdot b)^n = a^n \cdot b^n
\]

In this case, the expression inside the parentheses is \( -2p^4 \), so distribute the exponent \( 5 \) to both parts:

\[
(-2)^5 \cdot (p^4)^5
\]

Now simplify each part:

1. \( (-2)^5 = -32 \) (since \( (-2) \cdot (-2) \cdot (-2) \cdot (-2) \cdot (-2) = -32 \))
2. \( (p^4)^5 = p^{4 \cdot 5} = p^{20} \)

Thus, the simplified expression is:

\[
-32p^{20}
\]

Would you like more details or have any questions?

Here are some related questions for further practice:

1. Simplify \( (3p^2)^4 \).
2. What is \( (-3x^3)^2 \)?
3. Expand \( (4a^5)^3 \).
4. How would you simplify \( (5m^6)^2 \)?
5. Simplify \( (-p^7)^3 \).

**Tip**: When raising a product to a power, remember to apply the exponent to each factor separately.

Learn how to simplify the expression (-2p^4)^5 by applying the power of a product rule. This solution demonstrates the step-by-step process of distributing exponents and simplifying algebraic expressions, suitable for students in Grades 9-10.

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