Explanation:

Exponentiation

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)

$Description: a^n = \underbrace{a \times \cdots \times a}_n,$

just as multiplication by a positive integer corresponds to repeated addition

$Description: a \times n = \underbrace{a + \cdots + a}_n.$

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

$Description: \frac{a^n}{a^m} = a^{n - m}.$

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

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

$Description: 1 = \frac{a^n}{a^n} = a^{n - n} = a^0$

(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:

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

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

http://en.wikipedia.org/wiki/Exponentiation

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