Recently, a student of mine, while learning exponentiation, asked me "but what does 'exponent' mean?" Like all questions I am unable to answer, I immediately became obsessed with answering it.

The process of exponentiation, of course, hasn't been around forever. The ancient Greeks started it all with their obsession with geometry, in which squaring and cubing numbers figured prominantly. The area of a square, for example, is x squared, and the area of a cube is x cubed (where x is the length of a side.) "x squared" was taken to mean x·x and "x cubed" was taken to mean x·x·x.

It wasn't until Diophantus of Alexandria (250 A.D.) that we saw the use of symbols to represent exponentiation, and he only had symbols for x^-6 to x⁶, inclusive. Although this was a far cry from the usefullness of exponents of arbitrary size, it certainly improved the typography of algebra. It is worth noting that Diopantus' notation employed the use of the superscript, as we do today.

No further improvements were made in algebraic notation until Nicolas Oresme in the 14^th century. This is hardly surprising considering the Middle Ages stretched between Diophantus and Oresme, casting mathematics into pitch blackness. While Oresme's notation may appear daft to us today, it was remarkable in that it allowed for arbitrary exponents (written as arabic numerals.)

The notation we use today, xⁿ, was introduced by Réne Descartes in the 17^th century, along with such important ideas as the Cartesian plane (Descartes' Latin name was Cartesius.) At first I suspected that Descartes was the first to use the term exponent, but it appears that one of the Bernoullis (Johann, Jakob, Daniel or Nicolaus II) may have used it first. At any rate, that dates the use of the term to the 17^th century.

The term itself comes from the Latin expone, "to put forth." That is, the exponent tells you how many times to "put forth" the base.