How to proof x^0=1?

Answer 1

Law of exponents is the more easily understood, and straightforward way to show this.

x^a/x^b = x(a - b)

Right?

So....if a = b, then you have:

x^a/x^a = 1 = x^(a - a) = x^0

The first part of that last step is like saying 2/2 = 1, or 5/5 = 1, or z/z = 1

Therefore: x^0 = 1

Make sense?

:)

Answer 2

ANY number to the power of 0 equals 1.
ex. 10^2= a 1 with 2 zeros after it
10^3= a 1 with 3 zeros after it
10^1= a 1 with 1 zero after it
10^0= a 1 with 0 zeros after it

Answer 3

x^1 =x that is given, then by default x^0 = x^1/x, which would be x/x which equals 1

Answer 4

example..x^0= x^(a-a) = x^a/ x^a =1

Answer 5

x^0 = 1
this is the same as saying
(x^n)/(x^n) = x^(n - n) = x^0

as you can see, since there are 2 identical values on top and bottom, you get 1.

For ex:

x = 2 and n = 3

(x^n)/(x^n)
(2^3)/(2^3)
8/8
1

Also in case you didn't know, when you have exponents with like coefficents, and you are dividing them, all you do is take the exponents and subtract them like i have done above.

Answer 6

joe_ska,your proof looks good but I believe there is an error in it as multiplying by 0 is not an equivalent operation.

Answer 7

Take 'log' on both sides.

logx^0 = log1
as 0=0
so proved. (just for fun)

Answer 8

suppose ln(x) = y
then:
0*ln(x) = 0*y
ln(x^0) = 0
exp(ln(x^0)) = exp(0)
and finally
x^0 = 1

Maybe?

Answer 9

Grab any scientfic calculator and you can find the answer But that probably isn't what you want to know.

Answer 10

x=x^1
1/x=x^-1
x(1/x)=(x^1)*(x(^-1)=x^(1-1)=x^0=x/x=1