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To solve this problem using the distributive property, we need to multiply \( 9z^4 \) by each term inside the parentheses. The expression given is:

\[
9z^4 \cdot (10z + 8z^4)
\]

### Step-by-Step Solution:
1. **Distribute \( 9z^4 \):**
   - First, multiply \( 9z^4 \) by \( 10z \):
     \[
     9z^4 \cdot 10z = 9 \times 10 \times z^4 \times z = 90z^{4+1} = 90z^5
     \]
   - Next, multiply \( 9z^4 \) by \( 8z^4 \):
     \[
     9z^4 \cdot 8z^4 = 9 \times 8 \times z^4 \times z^4 = 72z^{4+4} = 72z^8
     \]

2. **Combine the terms:**
   \[
   90z^5 + 72z^8
   \]

### Final Simplified Expression:
\[
72z^8 + 90z^5
\]

You can also write it in the standard polynomial form as:
\[
72z^8 + 90z^5
\]

Would you like further details on any of these steps, or do you have any questions?

Here are 5 related questions to expand your understanding:
1. What is the distributive property, and why is it useful in algebra?
2. How do you simplify expressions involving exponents?
3. What happens when you multiply terms with the same base but different exponents?
4. Can the distributive property be used with more than two terms inside the parentheses?
5. How do you factor out the greatest common factor from a polynomial?

**Tip:** When using the distributive property, always pay attention to both coefficients and exponents to avoid errors in your calculations.

Use the distributive property to remove the parentheses. Simplify your answer as much as possible: 9z^4(10z + 8z^4)

Learn how to apply the distributive property to simplify the expression 9z^4(10z + 8z^4). This step-by-step guide explains how to multiply terms with exponents, combine like terms, and achieve the final simplified expression. Suitable for students in Grades 9-11.

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