Difference between revisions of "Exponential Properties"
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* For any nonzero number <math> a </math>, <math> a^0 = 1 </math>. | * For any nonzero number <math> a </math>, <math> a^0 = 1 </math>. | ||
* For any positive number <math> m </math>, <math> 0^m = 0 </math>. | * For any positive number <math> m </math>, <math> 0^m = 0 </math>. | ||
| − | * <math> 0^m </math> does not exist when m is negative (since <math> 0^{-n} = 1/0^n = 1/0 </math>), <math> 0^ | + | * <math> 0^m </math> does not exist when m is negative (since <math> 0^{-n} = 1/0^n = 1/0 </math>), and <math> 0^m </math> is either undefined or indeterminate when <math> m = 0 </math> (that is, <math> 0^0 </math> is undefined or indeterminate depending on the context). |
==Resources== | ==Resources== | ||
* [https://tutoring.asu.edu/sites/default/files/exponentialandlogrithmicproperties.pdf Exponential and Logarithmic Properties], Arizona State University | * [https://tutoring.asu.edu/sites/default/files/exponentialandlogrithmicproperties.pdf Exponential and Logarithmic Properties], Arizona State University | ||
Revision as of 13:05, 16 September 2021
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 , and .
- Product of like bases: For
Special exponential properties involving 0:
- For any nonzero number , .
- For any positive number , .
- does not exist when m is negative (since ), and is either undefined or indeterminate when (that is, is undefined or indeterminate depending on the context).
Resources
- Exponential and Logarithmic Properties, Arizona State University
