You are here:

Algebra/Mr.David Montiel,

Advertisement

Expert: - 9/10/2009


Question
can you please verify why any variable or number having power zero equals to one?

Answer
There are many ways to show this, but I like the following one.

I'm assuming you are familiar with the identity:

(a^m)/(a^n)=a^(m-n)          ...(1)

"^" means "to the power of".

Also, would you agree that, for any number "x" that is NOT zero:

x/x=1                        ...(2)

Now, let's write "x" as a number to the power of another number

x = a^m

So far so good? Then we rewrite (2) as

x/x = (a^m)/(a^m) = 1

But from equation (1) we know that

(a^m)/(a^m) = a^(m-m)

but, clearly  m-m = 0. So

a^(m-m) = a^0 = 1

We have shown that a^0. Since we didn't specify the value of "a", this should be true for any
number (except a=0).

There is no consensus on what the value of 0^0 is. I'd advice you have a look at the following link for more info:

http://en.wikipedia.org/wiki/Exponentiation

Hope this is clear.

Cheers,
David

Algebra

All Answers

Answers by Expert:

Ask Experts

Volunteer

David Montiel

Expertise

PLEASE READ THIS BEFORE POSTING YOUR QUESTION: While I am glad to offer HELP with problems, I refuse to SOLVE problems. There is a difference. Please do not just copy a question from a texbook or assignment. I WILL REJECT IT. I will only accept questions if, in addition to the statement of the problem, you describe in detail what you have tried so far in order to solve it, and what exactly is the problem you are encountering. In other words where/why are you stuck? I can answer questions at the level of the first couple of undergraduate years (in science and engineering) or below. You can ask me about algebra, trigonometry, basic probability and statistics, calculus, vector calculus, differential equations and Fourier analysis. I will not answer advanced (at the graduate level) math questions. Questions in Spanish are also welcome.

Experience

Over 8 years of private tutoring in Math and Physics. Five years as a Teaching Assistant in Physics.

Education/Credentials
BSc in Chemical Engineering. MSc in Chemical Physics. PhD in Physics.

©2012 About.com, a part of The New York Times Company. All rights reserved.