Question

When this exponent is applied to a nonzero base, the result is always 1

Answer 1

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 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.

Answer 2

When the exponent zero is applied to a nonzero base, the result is always 1.

$1^0 = 1\\2^0=1\\3^0=1\\...$