In the Middle Ages, writing or reading large numbers required many symbols or words and therefore took a great deal of time. This became a concern from the 12th century onward. Around 1500, the mathematician Chuquet set out to devise terminology for all these numbers, introducing the long-scale system (see the article "Trillions, zillions and myriads: the dizzying world of large numbers"). Later, the use of exponentiation in particular helped to overcome some of these obstacles. It is defined as repeated multiplication:
ab = a × a × a × …. × a
where the factor a is written b times.
This notation is relatively recent. As late as the end of the 16th century, Viète still used the words quadratum, cubum and quadrato-quadratum for the square, the cube and the fourth power. The first exponents appeared with René Descartes some fifty years later.
This innovation was decisive, since it made it possible to write a number such as
