Properties of Rational Exponents

Vocabulary flashcards covering the definitions and examples for the properties of rational exponents.

Product of powers

A property stating that $a^m \cdot a^n = a^{m+n}$. For example, $5^{1/2} \cdot 5^{3/2} = 5^2 = 25$.

Power of a power

A property stating that $(a^m)^n = a^{mn}$. For example, $(3^{5/2})^2 = 3^5 = 243$.

Power of a product

A property stating that $(ab)^m = a^m b^m$. For example, $(16 \cdot 9)^{1/2} = 16^{1/2} \cdot 9^{1/2} = 12$.

Negative exponent

A property stating that $a^{-m} = \frac{1}{a^m}$, where $a \neq 0$. For example, $36^{-1/2} = \frac{1}{36^{1/2}} = \frac{1}{6}$.

Zero exponent

A property stating that $a^0 = 1$, where $a \neq 0$. For example, $213^0 = 1$.

Quotient of powers

A property stating that $\frac{a^m}{a^n} = a^{m-n}$, where $a \neq 0$. For example, $\frac{4^{5/2}}{4^{1/2}} = 4^2 = 16$.

Power of a quotient

A property stating that $\frac{a}{b}^m = \frac{a^m}{b^m}$, where $b \neq 0$. For example, $\frac{27}{64}^{1/3} = \frac{27^{1/3}}{64^{1/3}} = \frac{3}{4}$.