EDGE Math 8

Laws of Exponents

In the solutions of the example in the previous slide, it appears that the exponents were subtracted when expressions with the same base were divided. This established the next law of exponents.

Quotient Rule
If $a$ is a nonzero real number and $m$ and $n$ are positive integers, then

$\frac{a^{m}}{a^{n}} = {\begin{cases} \end{cases}$	$a^{m - n}$	if m > n,
	1	if m = n, or
	$\frac{1}{a^{n - m}}$	if m < n.

This rule states that when dividing two exponential expressions with the same base, you just need to subtract the exponents.

Example

Simplify each expression.

1. $\frac{3^{5}}{3^{2}}$

2. $\frac{a^{4}}{a^{4}}$

3. $\frac{y^{4}}{y^{7}}$

Solution

1. $\frac{3^{5}}{3^{2}} = 3^{5 - 2} = 3^{3} = 27$

2. $\frac{a^{4}}{a^{4}} = 1$

3. $\frac{y^{4}}{y^{7}} = \frac{1}{y^{7 - 4}} = \frac{1}{y^{3}}$