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

Resources

• Exponential and Logarithmic Properties, Arizona State University