How do you simplify $\frac{x}{x^{3}}$ $x/x^3$ ?

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Answer 1 · 2015-07-09T08:52:20

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

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

The rule is:

$\frac{x^{a}}{x^{b}}$ $x^a/x^b$ = $x^{a - b}$ $x^(a-b)$

The question is to simplify

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

Using the rule,

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

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

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

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