EDGE Math 8

Consider the following expression, where $b \neq 0$ :

{(\frac{a}{b})}^{3} = \frac{a}{b} \cdot \frac{a}{b} \cdot \frac{a}{b} = \frac{a^{3}}{b^{3}}

Thus, ${(\frac{a}{b})}^{3} = \frac{a^{3}}{b^{3}} .$ This example illustrates the following law of exponents:

Rule for a Quotient Raised to a Power
If $a$ and $b$ are real numbers, with $b \neq 0,$ and if $m$ is a positive integer, then

{(\frac{a}{b})}^{m} = \frac{a^{m}}{b^{m}} .

This rule states that when raising a fraction to a power, you need to raise both the numerator and the denominator to that power.