To simplify the expression:

$\frac{a^8b^9}{9a^6b^7}$

Follow these steps:

1. Simplify powers of $a$:

$\frac{a^8}{a^6} = a^{8-6} = a^2$

2. Simplify powers of $b$:

$\frac{b^9}{b^7} = b^{9-7} = b^2$

3. The constant remains as is:

$\frac{1}{9}$

Thus, the simplified expression is:

$\frac{a^2b^2}{9}$

Would you like a more detailed explanation or have any questions about this simplification?

Here are some related questions:

1. How do you handle negative exponents in algebraic expressions?
2. What is the rule for dividing exponents with the same base?
3. How do you simplify expressions involving fractions and powers?
4. What is the difference between multiplying and dividing expressions with exponents?
5. How do you deal with higher powers of variables in polynomials?

Tip: Always subtract the exponents when dividing terms with the same base.