# How do you simplify (4x^-1)/(12x^2)?

May 21, 2018

$\frac{1}{3} {x}^{-} 3$

#### Explanation:

We have the following:

$\frac{\textcolor{p u r p \le}{4} \textcolor{b l u e}{{x}^{-} 1}}{\textcolor{p u r p \le}{12} \textcolor{b l u e}{{x}^{2}}}$

We can handle these expressions separately. The purple terms just simplify to

$\textcolor{p u r p \le}{\frac{1}{3}}$

And we can rewrite the blue expressions as follows:

$\textcolor{b l u e}{{x}^{- 1 - 2}}$

We have the same base on the top and bottom, so we can subtract the exponents. Thus, we have

$\textcolor{b l u e}{{x}^{-} 3}$

Putting it all together, we get

$\frac{1}{3} {x}^{-} 3$