Lesson 4: Raising Fractions to Powers

Property

If $a$ and $b$ are real numbers, $b \neq 0$, and $m$ is a counting number, then

To raise a fraction to a power, raise the numerator and denominator to that power.

Examples

• To simplify $\left(\frac{2}{3}\right)^4$, you apply the exponent to both the numerator and the denominator: $\frac{2^4}{3^4} = \frac{16}{81}$.

• To simplify $\left(\frac{p}{q}\right)^7$, you raise both the numerator and denominator to the 7th power, resulting in $\frac{p^7}{q^7}$.

Property

When a fraction is raised to the power of -1, it equals the reciprocal of the original fraction:

Examples

Property

When a fraction has a negative exponent, flip the fraction and make the exponent positive:

Examples