introducing 0th power

Let a be a number not equal to zero. Then for all n, we have that an is the product of a with itself n . Using the fact that the integer 1 is a multiplicative identityPlanetmathPlanetmath, (a1=a for any a), we can write


where we have used the properties of exponents under multiplication. Now, after canceling a factor of an from both sides of the above equation, we derive that a0=1 for any non-zero number.

Title introducing 0th power
Canonical name Introducing0thPower
Date of creation 2013-03-22 13:24:20
Last modified on 2013-03-22 13:24:20
Owner mathcam (2727)
Last modified by mathcam (2727)
Numerical id 8
Author mathcam (2727)
Entry type Topic
Classification msc 00A05
Related topic EmptyProduct