# How do you simplify (32x^3y)/y^9div(8x^4)/y^6?

Aug 30, 2017

Incorporate exponent variable laws and standard arithmetic simplification.

#### Explanation:

First, as a division expression, we're going to multiply the fractions. This involves reciprocating the second fraction.

$\frac{32 {x}^{3} y}{{y}^{9}} \div \frac{8 {x}^{4}}{{y}^{6}}$

$= \frac{32 {x}^{3} y}{{y}^{9}} \times \frac{{y}^{6}}{8 {x}^{4}}$

Now, we simplify normally.

$= \frac{32 {x}^{3} {y}^{7}}{8 {x}^{4} {y}^{9}}$

Now comes the most potentially confusing part. When you are simplifying variables in fractions, if you divide the numerator by the denominator of the same variable - but different degree, the resulting variable will be positioned in the numerator. The same goes for the denominator. This is something your teacher should teach so you are provided more examples.

Back to the expression, we're going to simplify the easiest of them all - the number.

$= \frac{4 {x}^{3} {y}^{7}}{{x}^{4} {y}^{9}}$

AND NOW COMES THE VARIABLES. First, the $x$ variable.

$= \frac{4 {y}^{7}}{x {y}^{9}}$

We'll do the same with the $y$ variable.

$= \frac{4}{x {y}^{2}}$

And that's it.

Hope this helps :)