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Example: Simplify Using Laws of Exponents

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Exponentiation is a mathematical operation, written as an, involving two numbers, the base a and the exponent (or power) n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors of a (the product itself can also be called power)

just as multiplication by a positive integer corresponds to repeated addition


Exponents one and zero

Notice that a1 is the "product" of only one a, which is defined to be a. Also note that an − 1 = an/a. Assuming n = 1, we get a0 = 1. Another way of saying this is that when n, m, and n m are positive (and if a is not equal to zero), one can see that

(Our solved example in mathguru.com uses this concept)

Extended to the special case when n and m are equal, the equality would read

(Our solved example in mathguru.com uses this concept)

since both the numerator and the denominator are equal. Therefore we take this as the definition of a0. This leads to the following rule:

1.       Any number raised to the power 1 is the number itself.

2.       Any nonzero number raised to the power 0 is 1. (Our solved example in mathguru.com uses this concept)




The above explanation is copied from Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons Attribution- ShareAlike 3.0 Unported License.