What do the little numbers in math mean, and how do they work?

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Like these: $^{1 \ 2 \ 3 \ 4 \ 5 \ 6 \ 7 \ 8 \ 9}$.

They are little numbers aside the regular sized unicode characters, and you see them pop up in equations as follows: $$1 + 1^9 \times 33^9(3) = {?}.$$ What do the tiny/little digits mean, and how do they work and make sense?

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Those little numbers are called exponents. They work by multiplying the number below them by itself $n$ times, where $n$ is the exponent. For example $$2^3=2\cdot2\cdot2=8$$ $$14^2=14\cdot14$$ Also you can take as a definition that $x^0=1$ for any number $x$.

You can find more informations about exponentiation in the Wikipedia page.