Math Logic 


Question : 
Why
is it that any number raised to the power zero is equal to 1
and not zero ? 
Answer : 
When a number is raise to the power 0, we are not actually
multiplying the particular number by 0. For example, let us
take 2^{0}. In this case we are not actually multiplying
the number 2 by 0.
We define 2^{0} = 1, so that each power of 2 is one factor of 2 larger than the last, e.g., 1,2,4,8,16,32... 
This involves the rules of exponents
particularly division.
If a is a number and x and y are also numbers, then
according to the rule of division for powers with the same base,
a^x/a^y = a^(x  y).
It says the quotient of two powers with the same base is equal to the common base raise to
the exponent equal to the difference between x and y.
So, if x = y, then a^x/a^y = a^(x y) = a^0
But a^x is equal to a^y, since x = y; hence a^x/a^y = 1
Therefore, by Transitive property of Equality,
a^0 = 1
Thus, this result says that number raised to the power zero is equal to 1.

