Let's simplify the expression:

$\frac{15a^6b^4}{-3ab}$

Step-by-step:

1. Simplify the coefficients: $\frac{15}{-3} = -5$

2. Simplify the powers of $a$: $\frac{a^6}{a} = a^{6-1} = a^5$

3. Simplify the powers of $b$: $\frac{b^4}{b} = b^{4-1} = b^3$

So, the simplified expression is:

$-5a^5b^3$

Final Answer:

$\boxed{-5a^5b^3}$

Would you like further clarification on any part of this?

Here are some related questions for further practice:

1. How do you simplify powers with negative exponents?
2. What happens when you divide monomials with the same base?
3. How can you simplify expressions with more than two variables?
4. What is the general rule for simplifying rational expressions?
5. How do you handle terms with different powers of the same variable in fractions?

Tip: Remember to subtract the exponents when dividing terms with the same base (e.g., $a^m / a^n = a^{m-n}$).