can anyone help me to explian why 2^0=1?

Question

I know that this statement is true but i need to know how to prove it in a mathmatical statement
2^0=1
or two to the power of zero equals one

Answer 1

Look this

2^3 = 8

2^2 = (2^3)2 = 8/2 = 4

2^1 = (2^3)/2^2 = 8/4 =2

2^0 = (2^3)/2^3 = 8/8 = 1

2^-1 = (2^3)/2^4 = 8/16 = 1/2


Or you can do this

x^y/x^y=1

x^y/x^y = x^y*x^-y = x^0

So if x^y/x^y = x^0 and x^y/x^y=1
x^0 =1

Bye

Abraço

Answer 2

A law of exponents is a^m / a^n = a^(m - n).

For example,

2^7 / 2^3 = 2^(7 - 3) = 2^4 = 16

2^6 / 2^5 = 2^(6 - 5) = 2^1 = 2

If a number x is not zero, then x / x = 1.

For example,

5 / 5 = 1

2^3 / 2^3 = 1

Take that last equation and turn it around...

1 = 2^3 / 2^3 = 2^(3 - 3) = 2^0

Therefore, 1 = 2^0 or 2^0 = 1.

Answer 3

2 is an entity. It's like a variable. To the 0 power, mean's it's not being exponentialled or multiplied by anything. It is unto itself.

If its exponential is say, 1, then it is multiplied by itself, which is 2. So, then it would be 2 * 2. If the exponent is larger and say it is 5, then it would be 2 times itself 5 times. That would mean:
2 * 2 * 2 * 2 * 2. And THAT translates to: 2 * 2 =4 * 2 = 8 * 2 and eventually it equals 32. Do not multiply exponents as if they're equal variables. (Like, 2^0 = 0).
So, 2 not exponentialized to anything is 1 BECAUSE you're counting the number of the variable, which is simply the number 2. 2 to the first exponent is 2 because 2 exponentialized once is simply itself. If the exponent is 2, then its two times itself, which is then 4.
Hope this helps!

Answer 4

note:

2^4 = 16

2^3 = 8 [which is 16/2 or (2^4)/2 ]

2^2 = 4 [ which is 8/2 or (2^3)/2 ]

2^1 = 2 [ which is 4/2 or (2^2)/2 ]

so, 2^0 = 1 [which following the same logic is 2/2 or (2^1)/2 ]

The general rule is that any number, except zero, to the zero power = one

0^0 is undefined

Answer 5

2^4 = 16
2^3 = 8
2^2 = 4
2^1 = 2
2^0 = 1
It would appear to be reasonable on basis of above.

Answer 6

Well, first off, anything to the first power is that number, correct? (x^1=x). And anything squared is that number times itself. (x^2=x*x). So, basically what's happening is you're multiplying the number by... well something. When it's cubed, you multiply the number 3 times (x*x*x), and when it's cubed, you do the same thing twice, so when it's to the first power, you're just sort of multiplying the number by 1, and when it's to the power or zero, you're basically multiplying it by nothing. Zero is technically nothing, so in a sense you're multiplying your number by zero, and as simple multiplication tells us, anything times zero is zero.

Hope that helped.

Answer 7

http://mathforum.org/dr.math/faq/faq.0.to.0.power.html

requires calculus knowledge. but thats one of the best i've seen.