Exponential Properties

Introduction

Exponential properties can be used to manipulate equations involving exponential expressions and/or functions. Here are some important exponential properties:

• Negative exponent property: For any number $a$, $a^{-n}={\frac {1}{a^{n}}}$ and ${\frac {1}{a^{-n}}}=a^{n}$.
• Product of like bases: For

Special exponential properties involving 0:

• For any nonzero number $a$, $a^{0}=1$.
• For any positive number $m$, $0^{m}=0$.
• $0^{m}$ does not exist when m is negative (since $0^{-n}=1/0^{n}=1/0$), $0^{n}$ and is either undefined or indeterminate when $n=0$ (that is, $0^{0}$ is undefined or indeterminate depending on the context).

Resources

• Exponential and Logarithmic Properties, Arizona State University