Question

why is any number raised to the power zero is 1 ?

Answer 1

"When a number is raise to the power 0, we are not actually multiplying the particular number by 0. For example, let us take 20. In this case we are not actually multiplying the number 2 by 0.

We define 20 = 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." From this site http://www.calculatoredge.com/math/mathlogic/logicans4.htm

Answer 2

if you see you end up basically dividing by two as you go down therefore you end up with 1 at the power of zero