Why is anything raised to the power of zero is 1 not 0?

Question

Examples:

2^0 = 1
3^0 = 1
4^0 = 1

Answer 1

Actually in multiplication form, 2^2 would be 1x2x2. There's no point of putting the one because 2x2 = 1x2x2. When it's 2^0, there's no two's but still, the 1 is there so the answer is one.

Answer 2

"something to the skill 0" rule: something to the skill 0 is in simple terms "one million". Why is this so? there are countless motives. One may well be reported as "because of the fact that is how the regulations artwork out." yet another could be to track via a progression like here: {'^' skill to skill of} 3^5 = 3^6 ÷ 3 = 243 3^4 = 3^5 ÷ 3 = eighty one 3^3 = 3^4 ÷ 3 = 27 3^2 = 3^3 ÷ 3 = 9 3^one million = 3^2 ÷ 3 = 3 Then logically 3^0 = 3^one million ÷ 3 = 3 ÷ 3 = one million. yet another remark: Please do not inquire from me to "define" 0^0. There are a minimum of two techniques of finding at this volume: something to the 0 skill is "one million", so 0^0 = one million. 0 to any skill is 0, so 0^0 = 0.

Answer 3

Have you learned how to divide x squared by x squared? You know the answer is 1.

Now, in algebra, when you divide like bases (the x) you subtract the exponents.

x to the 5th power divided by x to the second is x to the third

x^5/x^2= x^(5-2)= x^3

so if you are dividing x^2 by x^2 you get x^(2-2) =x^0, but since you know anything divided by itself is 1, then x^0 must =1


This works whether you are dividing variables, or numbers.

4^3/4^3= 4^(3-3)=4^0=1

Answer 4

Because powers are to do with multiplying numbers together
5^3 = 5 x 5 x 5

The "do nothing" number for multiplication is 1, so we _define_ 5^0 to be 1 - this is handy so that e.g.
5^2 x 5^4 = 5^6 x 5^0.

To annoy your teacher (I'm presuming you're at school, apologies if not), point out that:
- anything raised to the 0th power is 1
- 0 raised to anything is 0
- so what's 0 raised to the 0th power?

Contrast with multiplication of numbers, which is to do with "adding", e.g.
5 * 3 = 5 + 5 + 5
The "do nothing" number for addition is 0...

Answer 5

Think of it this way:

3^7 / 3^2 = 3^(7-2) or 3^5 = 243

Now dig this: Anything divided by itself = 1 or 6561 / 6561
6531 = 3^8

Try 3^8 / 3^8 = 3^(8-8) = 3^0 or 1

Make up your own, it's fun!

Answer 6

Because of the following:

x^2/x^2 = 1

---right?---

By the law of exponents: x^2/x^2 = x^(2 - 2)

Therefore x^(2 - 2) = 1, but x^(2 - 2) = 0

Then x^0 = 1



Make sense?

Answer 7

Think of it this way:

2^2/2^2=2^2-2=2^0

But, if we look at the expanded version....
(2)(2)/(2)(2)=1

Since they are equal, 2^0=1

Answer 8

Think about it this way.....

27, 9, 3, _, 1/3, 1/9

what goes in the blank? It would be 1, because that follows the pattern.

Answer 9

View this link. It explains why.
http://www.homeschoolmath.net/teaching/zero-exponent-proof.php

Answer 10

2^0=2^(1-1)=(2^1)/(2^1)=2/2=1
it is true for any other no.