Any number to the zero power is equivalent to?

Answer 1

1

proof:

n**3 * n**-3 = n**0

n**3 = n*n*n

n**-3 = 1/n * 1/n * 1/n

1/n * 1/n * 1/n * n * n * n= n*n*n/(n*n*n) = 1
Any number to the zero power = 1 .

Any number to the ' 1 ' power = itself .

Also:

ex. 3^0 = 1

but this is also the same value as :

5^0 = 1

Hence 3^0 = 5^0 = n^0 = 1

If you had 3^2 / 3^2 the result is 1 since any value divided by itself it 1.

Hence the base (here it's 3) and the exponent (here it's 2) is essentially eliminated and the result is just 1 as it would be for any other base and exponent. Mathematically, in an expression form you can eliminate (set to 0) the exponent by subtracting the exponents:

3^2 / 3^2 = 1 = 3^(2-2) = 3^0 = 1 = n^0
X^0=1

How about this:

If you had 5^2 / 5^2 , it equal 1 since any number divided by that same value is one. Therefore there is no power of 5 left since 5^1 would be 5. It is as if you subracted the exponents: 5^(2-2) = 5^0. This is valid because if you had something like:

5^2 / 5^1 = 5^(2-1) = 5^1

25 / 5 = 5 = 5^1