# How do you simplify \frac { - 24x ^ { 5} y ^ { 3} } { 8x ^ { 2} y ^ { 8} }?

May 15, 2018

This can be simplified to $\frac{- 3 {x}^{3}}{y} ^ 5$.

#### Explanation:

This fraction is easier to solve if we break it down into many pieces. We can simplify these pieces individually and then combine them at the end.

$\frac{- 24 {x}^{5} {y}^{3}}{8 {x}^{2} {y}^{8}} = \frac{- 24}{8} \cdot {x}^{5} / {x}^{2} \cdot {y}^{3} / {y}^{8}$

First, we will solve the constant term through simply division.

$\frac{- 24}{8} = - 3$

Next, we will solve the $x$ term.

${x}^{5} / {x}^{2}$

When dividing exponents, we subtract the exponent of the bottom number from the exponent of the top number.

$5 - 2 = 3$

${x}^{3}$

Now, we will solve the $y$ term. We will follow the same pattern as before.

${y}^{3} / {y}^{8}$

$3 - 8 = - 5$

${y}^{-} 5 = \frac{1}{y} ^ 5$

Finally, we combine all the terms.

$- 3 \cdot {x}^{3} \cdot \frac{1}{y} ^ 5 = \frac{- 3 {x}^{3}}{y} ^ 5$