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 $a$, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle a^{-n} = \frac{1}{a^{n}} } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \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 $0^{-n}=1/0^{n}=1/0$). $0^{0}$ is indeterminate or undefined depending on the context).

Resources

• Exponential and Logarithmic Properties, Arizona State University