Difference between revisions of "Exponential Properties"
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==Introduction== | ==Introduction== | ||
Exponential properties can be used to manipulate equations involving exponential expressions and/or functions. Here are some important exponential properties: | Exponential properties can be used to manipulate equations involving exponential expressions and/or functions. Here are some important exponential properties: | ||
| − | * Negative exponent property: | + | * Negative exponent property: <math> a^{-n} = \frac{1}{a^{n}} </math> and <math> \frac{1}{a^{-n}} = a^{n} </math> |
| − | * Product of like bases: | + | * Product of like bases: <math> a^ma^n = a^{m+n} </math> |
| + | * Quotient of like bases: <math> \frac{a^m}{a^n} = a^ma^{-n} = a^{m-n} </math> | ||
| + | * Multiple powers: <math> (a^m)^n = a^{mn} = (a^n)^m </math> | ||
| + | * Product to a power: <math> (ab)^n = a^nb^n </math> | ||
| + | * Quotient to a power: <math> \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} </math> | ||
| − | Special | + | Special cases involving 0: |
* 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> | + | * For any positive number <math> m </math>, <math> 0^m = 0 </math>. |
| − | * <math> 0^ | + | * <math> 0^m </math> does not exist if m is negative (since <math> 0^{-n} = 1/0^n = 1/0 </math>). |
| + | * <math> 0^0 </math> is indeterminate or undefined 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 | ||
| + | * [https://www.khanacademy.org/math/cc-eighth-grade-math/cc-8th-numbers-operations/cc-8th-exponent-properties/a/exponent-properties-review Exponent Properties Review], Khan Academy | ||
Latest revision as of 13:48, 22 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: and
- Product of like bases:
- Quotient of like bases:
- Multiple powers:
- Product to a power:
- Quotient to a power:
Special cases involving 0:
- For any nonzero number , .
- For any positive number , .
- does not exist if m is negative (since ).
- is indeterminate or undefined depending on the context).
Resources
- Exponential and Logarithmic Properties, Arizona State University
- Exponent Properties Review, Khan Academy
