Hi,
I'm a 5th grade teacher and need some help with a base number raised to the power of 0 always being 1. My kids asked me why and I told them I'd find out.
Thanks for the help.
Sheila

 

Hi Sheila,

The reason that mathematicians use the convention that a base number raised to the power of 0 be 1 comes from an attempt to be consistent with the notation. There are some nice properties that come from our use of exponential notation. For example

53 x 54 = (5 x 5 x 5) x (5 x 5 x 5 x 5) = 57

so you can simplify 53 x 54 by just adding the exponents, 3 + 4 = 7.

Likewise if you use negative exponents

53 x 5-4 = (5 x 5 x 5) x ( 1/5 x 1/5 x 1/5 x 1/5) =  1/5 = 5-1

Again 53 x 5-4 can be simplifies by just adding the exponents, 3 + (-4) = -1.

So what about 53 x 5-3? We know that

53 x 5-3 = (5 x 5 x 5) x ( 1/5 x 1/5 x 1/5) = 1

and yet the addition of the exponents gives 3 + (-3) = 0. Hence if we are going to be consistent with the notation it makes sense to say

50 = 1.

It's not a "fact" like 1 + 1 = 2 but rather a convention that mathematicians use so that the simplification by adding exponents is true, even when the sum is 0.

I hope this helps,
Penny