What is 10^-(infinity)

All calculators I tried it on return 0, but I think it's rounded. I thought it should be infinitely small.

You have to be clear what you are asking here.
Normally when we calculate something like 10^(-3) or 10^(1.5) we are operating in the real number system. However, within the real number system there isn't a number called infinity so we can't calculate 10^-(infinity). I'm puzzled how you managed to enter it on a calculator as I've not seen a calculator with an infinity button. Perhaps the best way to give a meaningful answer is to say that you want to evaluate the limit of 10^-(n) as n approaches infiniity and this limit does equal 0. To show this properly you need to carefully define what you mean by a limit.

There is no such thing as a number which is infinitely small.

It is the Archimedian property of the real numbers that for any two non-equal values a and b, there exists a value between a and b. However, it is impossible to find a value between 0 and 10^-∞, hence they must be the same.

Dear Benimation,


10^(-I)

Remove the negative exponent in the numerator by rewriting 10^(-I) as (1)/(10^(I)). A negative exponent follows the rule: a^(-n)=(1)/(a^(n)).
(1)/(10^(I))

Any number raised to the power of - infinity results in a 0+.
Any number raised to the power of + infinity results in a + infinity.

GOD bless you...

10^-(infinity) = 1/10^(infinity) = 1/infinity = 0

Yup 10^-infinite is 0.

check this site out for proof.

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