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#25582 - 03/16/0301:50 AMWhy X to the power of 0 always equals 1

Joined: Mar 2002 Posts: 1,273SilentRage
DollarDNS Owner

Mathematicians *define* x^0 = 1 in order to make the laws of exponents work even when the exponents can no longer be thought of as repeated multiplication. For example, (x^3)(x^5) = x^8 because you can add exponents. In the same way (x^0)(x^2) should be equal to x^2 by adding exponents. But that means that x^0 must be 1 because when you multiply x^2 by it, the result is still x^2. Only x^0 = 1 makes sense here.