# How do you simplify (12mn)/( 12m^3n^5) using only positive exponents?

Oct 2, 2016

Subtract the exponents in the denominator from the exponents in the numerator.

#### Explanation:

Before we do anything, we can divide 12 by 12 and get rid of those numbers. We now have $\frac{m n}{{m}^{3} {n}^{5}}$.

Next, we can use the rule that says ${x}^{a} / {x}^{b} = {x}^{a - b}$. To make this easier, let's separate the fraction we have into two fractions:

$\frac{m}{m} ^ 3 = {m}^{1 - 3} = {m}^{-} 2 = \frac{1}{m} ^ 2$
$\frac{n}{n} ^ 5 = {n}^{1 - 5} = {n}^{-} 4 = \frac{1}{n} ^ 4$

We can now combine the two fractions together to get our answer, which is $\frac{1}{{m}^{2} {n}^{4}}$.