Section 2.4 Laws of Exponents
Here’s a summary of the Laws of Exponents encountered in this chapter.
| Zero Exponent:
\begin{equation*}
a^0 = 1, \quad a\neq 0
\end{equation*}
|
Unit Exponent:
\begin{equation*}
a^1 = a
\end{equation*}
|
| Power of Product:
\begin{equation*}
(a b)^n = a^{n} b^n
\end{equation*}
|
Power of Quotient:
\begin{equation*}
\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}
\end{equation*}
|
| Product of Powers:
\begin{equation*}
a^m a^n = a^{m+n}
\end{equation*}
|
Quotient of Powers
\begin{equation*}
\frac{a^m}{a^n} = a^{m-n}
\end{equation*}
|
| Reciprocal:
\begin{equation*}
a^{-1} = \frac{1}{a}
\end{equation*}
|
Negative Exponent:
\begin{equation*}
a^{-n} = \frac{1}{a^n}
\end{equation*}
|
| Power of Power:
\begin{equation*}
(a^m)^n = a^{mn}
\end{equation*}
|
Rational Exponent:
\begin{equation*}
a^{m/n} = \sqrt[n]{a^m} = \left(\sqrt[n]{a}\right)^m
\end{equation*}
|
