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 54 = (5 5 5) (5 5 5 5) = 57 so you can simplify 53 54 by just adding the exponents, 3 + 4 = 7. Likewise if you use negative exponents 53 5-4 = (5 5 5) ( 1/5 1/5 1/5 1/5) =  1/5 = 5-1 Again 53 5-4 can be simplifies by just adding the exponents, 3 + (-4) = -1. So what about 53 5-3? We know that 53 5-3 = (5 5 5) ( 1/5 1/5 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