The term exponent originates from the Latin exponentem, the present participle of exponere, meaning "to put forth". The term power ( See more

The exponentiation operation with integer exponents may be defined directly from elementary arithmetic operations.
Positive exponents
The definition of the exponentiation as an iterated multiplication can be formalized by using See more

For positive real numbers, exponentiation to real powers can be defined in two equivalent ways, either by extending the rational powers to reals by continuity (§ Limits of rational exponents, below), or in terms of the logarithm of the base and the exponential function See more

Antiquity
The Sand Reckoner
In The Sand Reckoner, Archimedes proved the law of exponents, 10 · 10 = 10 , necessary to … See more

The expression b = b · b is called "the square of b" or "b squared", because the area of a square with side-length b is b . (It is true that it could also be called "b to the second power", but "the square of b" and "b squared" are more traditional)
Similarly, the … See more

If x is a nonnegative real number, and n is a positive integer, $${\displaystyle x^{1/n}}$$ or $${\displaystyle {\sqrt[{n}]{x}}}$$ denotes … See more

In the preceding sections, exponentiation with non-integer exponents has been defined for positive real bases only. For other bases, difficulties appear already with the apparently simple case of nth roots, that is, of exponents $${\displaystyle 1/n,}$$ See more