Power Of 0 = 1 (Explain Please)

1. Nov 6, 2008

Nick-30

1. The problem statement, all variables and given/known data
For part of my homework i need to explain:
Why does any number with a power of zero have a value of 1?

2. Relevant equations
100^0=1
81^0=1
5^0=1

3. The attempt at a solution

2. Nov 6, 2008

mgb_phys

Look at the exponential sequence if you write down the positive and negative powers of a number
eg 3:
3^-3 = 1/27
3^-2 = 1/9
3^-1 = 1/3
3^0 = 1
3^1 = 3
3^2 = 9
3^3 = 27

What's the pattern between each value?

edit fixed formating

Last edited: Nov 6, 2008
3. Nov 6, 2008

4. Nov 6, 2008

Staff: Mentor

Check what happens if you multiply 3*1/27, 3*1/9...

5. Nov 6, 2008

Nick-30

Yeah but how do i explain why does any number with a power of 0 have a value of 1

6. Nov 6, 2008

Gokul43201

Staff Emeritus
1. Do you know how to expand $n^{b+c}$?

2. Now, if you set $b+c=0$, write b in terms of c, and repeat step 1, what do you get?

7. Nov 6, 2008

mgb_phys

Because if you divide "any number" by itself you get 1 and if you multiply "1/any number" by "any number". Just look at the above example with any other number than 3.

8. Nov 6, 2008

joeyar

You know the rules for adding/subtracting exponents?

(a^b)*(a^c) = a^(b+c)

and

(a^b)/(a^c) = a^(b-c).

What happens when b = c?

You get (a^b)/(a^b) = a^(b-b) = a^0. But if you look to the LHS, you will see we have a number divided by itself which is 1.

Incidentally, it is not true that 'any number' to the power of 0 = 1: 0^0 is undefined.

9. Nov 7, 2008

Дьявол

As others explained, ab*ac=ab+c. Now try for example:
3-1*31=3/3=1
Same if you write as:
3-1+1=30=1.

Do you know how to explain now?