# How do you simplify (15x^3y^-8)/(5x^2y^-4)?

Before we do anything, we can divide 15 by 3 and take care of those numbers. We now have $\frac{3 {x}^{3} {y}^{-} 8}{{x}^{2} {y}^{-} 4}$.
Next, we can use the rule that says x^a/x^b=x^a−b. To make this easier, let's forget about the number and separate the fraction we have into two fractions:
${x}^{3} / {x}^{2} = {x}^{3 - 2} = {x}^{1} = x$
${y}^{-} \frac{8}{y} ^ - 4 = {y}^{- 8 - - 4} = {y}^{-} 4 = \frac{1}{y} ^ 4$
We can now combine the two fractions and our number together to get our answer, which is $\frac{3 x}{y} ^ 4$.