Why anything to the power zero is 1?
for example, 55^0=1

Question

Why anything to the power zero is 1?
for example, 55^0=1

anonymous · Answer

Okay first of all $$
x^a\times x^b = x^c
$$What is $c$?

anonymous · Answer

In terms of $a$ and $b$, what is $c$?

anonymous · Answer

@tryder Do you know?

anonymous · Answer

not really.

anonymous · Answer

Experiment.

anonymous · Answer

$$
2^2\times 2^3=2^c
$$

anonymous · Answer

$$
2^2\times 2^2 = (2\times 2)\times (2\times 2\times 2) = 2^c
$$

anonymous · Answer

In this case, what is $c$?

anonymous · Answer

Hint: count.

anonymous · Answer

The empty product is 1.
When you multiply no numbers together you get 1.

If the empty product way not 1, multiplication would not make sense.

Multiplying 5 * 2, is the same as multiplying no numbers, then multiplying the result by 5 and then by 2.

So we have:
5 * 2 = empty product * 5 * 2

And the only way this is true, is if the empty product is 1.

So when raising to the power of zero, we are multiplying a number by itself zero times, which is the same as the empty product, so is equal to 1.

anonymous · Answer

thank you

anonymous · Answer

Oh wow, lol.

anonymous · Answer

When you multiply, the exponents are added: $$
x^a\times x^b=x^{a+b}
$$

anonymous · Answer

Suppose one of the exponents are $0$:$$
x^0\times x^b=x^{0+b}=x^b
$$

anonymous · Answer

$$
x^0\times x^b=x^b
$$Divide both sides by $x^b$:$$
x^0 = 1
$$

anonymous · Answer

thank you @wio for helping. sorry I didn't understand you in the beginning. I am not good at math

anonymous · Answer

In the beginning, there was no definition of the $0$ exponent.  The definition was chosen based on what would be consistent with current properties of exponents.