Let's break down the expression $(8a^5b^4 - 7a^3)(-5ab^2)$ and simplify it.

Step 1: Distribute $(-5ab^2)$ to both terms inside the parentheses.

We will use the distributive property, multiplying $(-5ab^2)$ by each term in the parentheses.

$= (8a^5b^4)(-5ab^2) + (-7a^3)(-5ab^2)$

Step 2: Multiply the terms.

• For $(8a^5b^4)(-5ab^2)$: $8a^5b^4 \times -5ab^2 = -40a^{5+1}b^{4+2} = -40a^6b^6$

• For $(-7a^3)(-5ab^2)$: $-7a^3 \times -5ab^2 = 35a^{3+1}b^{2} = 35a^4b^2$

Step 3: Combine the results.

The simplified expression is: $-40a^6b^6 + 35a^4b^2$

So, the final answer is:

$\boxed{-40a^6b^6 + 35a^4b^2}$

Would you like any additional details or clarifications? Here are some related questions for practice:

1. How do you apply the distributive property to binomials?
2. What are the rules for multiplying powers of the same base?
3. How would the answer change if the second factor was $-3ab$ instead of $-5ab^2$?
4. What is the degree of each term in the simplified expression?
5. Can you factor the expression $-40a^6b^6 + 35a^4b^2$?

Tip: When multiplying expressions with exponents, always add the exponents of like bases.