## A Conversation for Number Systems

### Why any number to the power 0 gives the answer 1

Ocean Soul (registered Linux user 390755) Started conversation Oct 8, 2001

Hi!

I just thought it try here to explain to non-mathematicians why any number to the power of 0 is 1, as mentioned in the entry.

When dealing with powers, there are three rules commonly used to simplify things. One of these states that any number raised to a power, divided by the same number raised to a power, is equal to the number raised to the difference between the powers. For example:

5^6/5^2 = 5^(6-2) = 5^4

The next stage in showing this, involves making both powers equal. For example:

5^3/5^3 = 5^(3-3) = 5^0

However, in that calculation, 5^3 (125) was divided by itself, and any number divided by itself = 1

So, what that shows is that 5^3/5^3 = 5^0 = 1

This calculation will remain true whatever numbers are used. So, to put it algebraiclly (I think that's spelt right):

a^b/a^b = a^(b-b) = a^0 = 1

Where a and b can be any numbers

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