The exponent is another name for index or power; it tells you how many times to multiply the number by itself.
It does not have to be a whole number (fractional values are used to represent roots, eg an exponent of ½ is equivalent to square root: 4^½ = √4 = 2).
Nor does it have to be positive (negative values are reciprocals, eg 2^-1 = ½, 2^-2 = 1/(2^2) = ¼).
It is also commonly used in scientific notation to mean the power of the 10 by which the number is multiplied to get it back into normal form. (This is particularly used with calculators and computers displaying numbers in scientific form where the number (with a single non-zero digit before the decimal point) is the mantissa and the power of 10 is the exponent.)
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the exponent is a negative
you don't have a zero exponent in math.
^ means, "to the exponent of"
i am not sure
12^2 or 122 not sure if this is what you mean.