The Laws of Exponents

By Contact e-mail icon (Published November 14th, 2008)

Copyright © 2008-2012 Exploring Binary

http://www.exploringbinary.com/the-laws-of-exponents/


For your reference, here is a summary of the laws of exponents:

  • \mbox{\small{\displaystyle {x^0 = 1}}}
  • \mbox{\small{\displaystyle {x^1 = x}}}
  • \mbox{\small{\displaystyle {x^a = \underbrace{x \cdot x \cdot \ldots \cdot x}_{a \: times}}}}}
    • Special case: \mbox{\small{\displaystyle {1^{a} = 1}}}
  • \mbox{\small{\displaystyle {x^{-a} = \frac{1}{x^a}}}}
    • Special case: \mbox{\small{\displaystyle {x^{-1} = \frac{1}{x}}}}
  • \mbox{\small{\displaystyle {\frac{1}{x^{-a}} = x^{a}}}}}
  • \mbox{\small{\displaystyle {{x^a} \cdot {x^b} = x^{a+b}}}}
  • \mbox{\small{\displaystyle {\frac{x^a}{x^b} = x^{a-b}}}}
  • \mbox{\small{\displaystyle {\left({x^a}\right)^{b} = x^{ab}}}}
  • \mbox{\small{\displaystyle {{\left(x \cdot y\right)}^a = x^a \codt y^a}}}
  • \mbox{\small{\displaystyle {\left({\frac{x}{y}}\right)^a = \frac{x^a}{y^a}}}}
    • Special case: \mbox{\small{\displaystyle {\left({\frac{1}{y}}\right)^a = \frac{1}{y^a}}}}
  • \mbox{\small{\displaystyle {x^{\frac{a}{b}} = \sqrt[b]{x^a}}}}
    • Special case: \mbox{\small{\displaystyle {x^{\frac{1}{b}} = \sqrt[b]{x}}}}
Dingbat
Grade: F (1 star)Grade: D (2 stars)Grade: C (3 stars)Grade: B (4 stars)Grade: A (5 stars) (2 votes, average: 5.00 out of 5)
Loading ... Loading ...

Related Articles

RSS feed icon
Get articles by RSS (What Is RSS?)
RSS e-mail icon
Get articles by e-mail
submit to reddit
«
»

Leave a Comment

(To reduce spam, cookies must be enabled)

You can follow any responses to this entry through the RSS feed.