The problem asks to simplify the expression $\frac{x^8y^9}{x^6y^6}$ and write the final answer without using negative exponents.

1. Problem Description

The problem asks to simplify the expression $\frac{x^8y^9}{x^6y^6}$ and write the final answer without using negative exponents.

2. Solution Steps

We can use the quotient of powers rule which states that $\frac{a^m}{a^n} = a^{m-n}$.

Applying this rule to the given expression, we have:

$\frac{x^8y^9}{x^6y^6} = \frac{x^8}{x^6} \cdot \frac{y^9}{y^6}$

Using the quotient of powers rule, we get:

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

$\frac{y^9}{y^6} = y^{9-6} = y^3$

Therefore,

$\frac{x^8y^9}{x^6y^6} = x^2y^3$

3. Final Answer

$x^2y^3$