text: Modern exponential notation In 1636, James Hume used in essence modern notation, when in L'algèbre de Vietè he wrote  for . Early in the 17th century, the first form of our modern exponential notation was introduced by René Descartes in his text titled La Géométrie; there, the notation is introduced in Book I.
  Some mathematicians (such as Descartes) used exponents only for powers greater than two, preferring to represent squares as repeated multiplication. Thus they would write polynomials, for example, as .
  "Indices"
  Samuel Jeake introduced the term indices in 1696. The term involution was used synonymously with the term indices, but had declined in usage and should not be confused with its more common meaning.
  Variable exponents, non-integer exponents
  In 1748, Leonhard Euler introduced variable exponents, and, implicitly, non-integer exponents by writing:
  Terminology
  The expression  is called "the square of " or " squared", because the area of a square with side-length  is . (It is true that it could also be called " to the second power", but "the square of " and " squared" are so ingrained by tradition and convenience that " to the second power" tends to sound unusual or clumsy.)
  Similarly, the expression  is called "the cube of " or " cubed", because the volume of a cube with side-length  is .