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

Feb 5, 2015

The answer is $x {y}^{6}$

Let's see how we get there.

First the long way. You can write ${y}^{2}$ as $y \cdot y$ etc.

$\frac{x \cdot x \cdot x \cdot x \cdot x \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y}{x \cdot x \cdot x \cdot x \cdot y \cdot y}$

Now cross out the $x$'s and $y$'s above and below the dividing bar two by two. You will be left with:

$x \cdot y \cdot y \cdot y \cdot y \cdot y \cdot y$ and nothing below the bar

This can be written as $x \cdot {y}^{6} = x {y}^{6}$

A shorter way would be to subtract the exponents:

First we rewrite: $\frac{{x}^{5} \cdot {y}^{8}}{{x}^{4} \cdot {y}^{2}} = {x}^{5} / {x}^{4} \cdot {y}^{8} / {y}^{2}$

${x}^{5} / {x}^{4} = {x}^{5 - 4} = {x}^{1} = x$ and ${y}^{8} / {y}^{2} = {y}^{8 - 2} = {y}^{6}$

Answer: $x \cdot {y}^{6} = x {y}^{6}$ (same answer of course)