Euclid discovered the concept underlying the exponent, calling the area of a square a power of the length of a single side. Archimedes later generalized the idea of powers in his work, "The Sand Reckoner." He discovered and proved the law of exponents in the same work.
A general exponential notation, however, was not invented until much later. Mathematicians in the Islamic golden age discovered algebra and worked with equations utilizing powers of two and three. The scholar Omar Khayyam developed a method for finding fourth, fifth and higher roots, but his method was geometric, not algebraic, and did not utilize any kind of exponential or root notation. Nicolas Chuquet, a European mathematician, was the first to use exponential notation and invent the radical symbol to represent roots. His work, "Triparty en la science des nombres," was written in 1484. René Descartes, almost two centuries later, popularized superscript notation for exponents and many other aspects of modern algebraic notation in Europe.