Let's simplify the given expression step by step:

$(4a^4b^4 - 7b^2) + (8a^4b - 6a^4b^4 + 5b^2)$

First, group like terms together. We'll look at the terms involving $a^4b^4$, $a^4b$, and $b^2$:

$= (4a^4b^4 - 6a^4b^4) + (8a^4b) + (-7b^2 + 5b^2)$

Now, simplify each group:

1. $4a^4b^4 - 6a^4b^4 = -2a^4b^4$
2. $8a^4b$ (no like term to combine with)
3. $-7b^2 + 5b^2 = -2b^2$

So, the simplified expression is:

$-2a^4b^4 + 8a^4b - 2b^2$

This is the final simplified form of the given expression.

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Would you like further details on the steps or have any questions about this? Here are some related questions you could explore:

1. How do we simplify expressions with exponents and multiple variables?
2. What are the rules for combining like terms in algebraic expressions?
3. How do you expand binomials in algebra?
4. How can we factor expressions similar to the one above?
5. How do we handle negative exponents in algebraic expressions?

Tip: Always group like terms first and simplify step by step to avoid confusion.