# How do you simplify  x/x^3?

Jul 9, 2015

$\frac{1}{x} ^ 2$

#### Explanation:

There is a rule when it comes to dividing exponents that have the same base; here, we have the common base of $x$.

The rule is:

${x}^{a} / {x}^{b}$=${x}^{a - b}$

The question is to simplify

$\frac{x}{x} ^ 3$
Note that this can be rewritten as ${x}^{1} / {x}^{3}$

Using the rule,

${x}^{1} / {x}^{3} = {x}^{1 - 3} = {x}^{-} 2 = \frac{1}{x} ^ 2$

(since ${x}^{-} a = \frac{1}{x} ^ a$)

Equivalently, you can divide the numerator and the denominator by $x$.