The answer is [tex]\frac{3}{5x^6y^6}[/tex].
Our original expression was
[tex]\frac{-9x^{-1}y^{-9}}{-15x^5y^{-3}}[/tex]
Negative exponents tell us to switch sides of the fraction; therefore they get moved as such:
[tex]\frac{-9y^3}{-15x^5x^1y^9}[/tex]
We can reduce the fraction we have:
[tex]\frac{3y^3}{5x^5x^1y^9}[/tex]
Using the product property of exponents we can combine the exponents on the denominator:
[tex]\frac{3y^3}{5x^6y^9}[/tex]
Using the division property of exponents, we subtract the exponents of y and get:
[tex]\frac{3}{5x^6y^6}[/tex]
