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Let's simplify the given expression step by step.

### The expression is:
\[
(-3p^4)(p^5)^5 + (-p^4)^4(4p^{13})
\]

#### Step 1: Simplify each part separately.

1. **First term: \((-3p^4)(p^5)^5\)**
   - \((p^5)^5 = p^{25}\) (because \((a^m)^n = a^{m \cdot n}\)).
   - Now, multiply \(-3p^4\) and \(p^{25}\):
     \[
     (-3p^4)(p^{25}) = -3p^{4+25} = -3p^{29}
     \]

2. **Second term: \((-p^4)^4(4p^{13})\)**
   - \((-p^4)^4 = p^{16}\) (since \((-1)^4 = 1\) and \((p^4)^4 = p^{16}\)).
   - Now, multiply \(p^{16}\) and \(4p^{13}\):
     \[
     p^{16} \cdot 4p^{13} = 4p^{16+13} = 4p^{29}
     \]

#### Step 2: Combine the terms:
Now, we have:
\[
-3p^{29} + 4p^{29}
\]

Since both terms have the same base \(p^{29}\), combine the coefficients:
\[
(-3 + 4)p^{29} = p^{29}
\]

### Final simplified expression:
\[
p^{29}
\]

Would you like more details or have any questions?

Here are 5 related questions for practice:
1. Simplify \((-2x^3)(x^2)^4 + (-x^3)^3(5x^6)\).
2. What is the result of \((2y^2)(y^5)^3 + (-y^2)^5(3y^{12})\)?
3. Simplify \((4a^6)(a^3)^2 + (-a^5)^3(2a^{10})\).
4. Combine like terms in \((-x^2)(x^4)^2 + (-x^3)^2(2x^7)\).
5. Simplify the expression \((-4z^5)(z^2)^3 + (-z^4)^4(3z^9)\).

**Tip**: When simplifying expressions with exponents, always apply the power rules first before combining like terms.

Simplify (-3p^4)(p^5)^5 + (-p^4)^4(4p^13)

Learn how to simplify the algebraic expression (-3p^4)(p^5)^5 + (-p^4)^4(4p^13) step-by-step. This problem covers key exponentiation rules, including the power of a power and the product of powers. Suitable for Grades 8-10.

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