Laws of Exponents

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The laws of exponents show the power of elementary algebra and lay the groundwork for logarithms. The laws are:


This Demonstration does not prove the first five of these laws; for a proof, you need to use mathematical induction.


Contributed by: George Beck (March 2011)
Open content licensed under CC BY-NC-SA



The laws of exponents apply to positive real numbers and and non-negative integers and . With proper attention to exceptional cases they may be extended to all real numbers and with even more care to complex numbers.

The number is as indeterminate as , because , and as such is properly a part of the study of limits in calculus, but to simplify statements in algebra it is sometimes convenient to formally define to be 1.

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