How do you prove 10^0 = 1?

We know that ---

x^a / x^a = 1

But from the law of indices we get --

=> x^(a-a) = 1

=> x^0 = 1

where x is any non-zero number. Now if we put x = 10 we get :-

=> 10^0 = 1 .................... Proved


Dr P.K.Tandon


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http://www.math.toronto.edu/mathnet/questionCorner/powerof0.html

there you go!

(10^2)/(10^2)
= 10^(2 - 2) (= 100/100)
= 10^0 (= 1)
= 1

10^(a-b)=10^a/10^b is true so if a=b 10^a/10^a=1


with numbers as an example

10^0=10^(3-3)=10^3/10^3 ------> the right side is 1

By laws of indices anything(except for 0) to the power of 0 is equal to1
Thus 10^0=1

use logarithms
log 10^0 = log 1
0log10 = log 1
0*1 =0
0 = 0

ok i will show you how to prove anything to the power of 0=1

1^1=1

1^1 divided by 1^1 = 1^(1-1) but 1 divided by 1 = 1

therefore 1^(1-1)= 1^0=1

therefore anything to the power of 0=1