3⁰ --3 to the power of 0-- equals what?

Question

3⁰ = 1 not zero or 3, but why does it equal one? Explain.

Answer 1

Anything to the power of zero equals one. This is because, in general x^m/x^n=x^(m-n), and so, x^m/x^m=x^(m-m)=x^0. And, since any number divided by itself equals one, x^m/x^m=x^0=1.

Answer 2

Any number raised to the power of Zero = 1.

So it follows that 3 ^ 0 = 1 & (-3) ^ 0 = 1.

Let 'a' be any number.

Divide a^ 5 by a ^ 5

What do you get?

a^5 / a^5 = a ^(5-5) = a ^ 0
{Theory of Indices: a^m divided by a ^ n = a ^ (m-n)}

But a^5 when divided by a^5 = 1. ( any number divided by itself = 1)

a ^ 0 = 1.

Is it clear?

Answer 3

Anything except 0 raised to the power 0 = 1, because that's what fits the pattern:

5^3 = 125
5^2 = 25
5^1 = 5 .........as exponent goes down by 1, result is divided by 5, so....

5^0 = 1.

here's another pattern:

5^4 / 5^2 = (5•5•5•5) / (5•5) = (5•5) = 5^2
you're just counting factors of 5. when you divide, shortcut is clearly subtract exponents, so...

5^2 / 5^2 = (5•5) / (5•5) = 1 = 5^(2-2) = 5^0

Answer 4

Anything to the zero power is one

The proof is usually something like

3^2/ 3^2 = 3^ 2-2= 3^0 which then =1

Since anything divided by itself is one (except 0) 0/0 is undefined, because division by zero is undefined.

If I had a better font, It would show up better. Put the exponents up higher, and you'll see how it works.