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: For any number <math> a </math>, <math> a^{-n} = \frac{1}{a^{n}} </math> and <math> \frac{1}{a^{-n}} = a^{n} </math>.
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* Negative exponent property: <math> a^{-n} = \frac{1}{a^{n}} </math> and <math> \frac{1}{a^{-n}} = a^{n} </math>
* Product of like bases: For
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* Product of like bases: <math> a^ma^n = a^{m+n} </math>
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* Quotient of like bases: <math> \frac{a^m}{a^n} = a^ma^{-n} = a^{m-n} </math>
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* Multiple powers: <math> (a^m)^n = a^{mn} = (a^n)^m </math>
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* Product to a power: <math> (ab)^n = a^nb^n </math>
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* Quotient to a power: <math> \left(\frac{a}{b}\right)^n = \frac{a^n}{b^n} </math>
  
Special exponential properties involving 0:
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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> 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> 0^0 </math> is indeterminate or undefined depending on the context).
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* <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
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* [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