Laws of Exponents

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

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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.

Exponent Laws (Wolfram MathWorld)

"Laws of Exponents" from The Wolfram Demonstrations Project
http://demonstrations.wolfram.com/LawsOfExponents/

Contributed by: George Beck

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