Become a math whiz with AI Tutoring, Practice Questions & more.

HotmathMath Homework. Do It Faster, Learn It Better.

Home

Power of a Quotient Property

This is similar to the power of a product property . Suppose you're dividing two expressions with the same exponent, but different bases.

By canceling common factors, you can see that:

Example 1:

$\frac{20^{3}}{4^{3}} = \frac{5 \cdot 4 \cdot 5 \cdot 4 \cdot 5 \cdot 4}{4 \cdot 4 \cdot 4} = 5^{3}$

Example 2:

Simplify ${(\frac{a}{6})}^{2}$ .

${(\frac{a}{6})}^{2} = \frac{a^{2}}{6^{2}} = \frac{a^{6}}{36}$

For all real numbers $a, b$ and $c$ (as long as $b \neq 0$ , and $a$ and $c$ are not both $0$ ):

$\frac{a^{c}}{b^{c}} = {(\frac{a}{b})}^{c}$

Popular Cities

Popular Subjects

;

Download our free learning tools apps and test prep books