Exponents indicate that a number should be multiplied by itself repeatedly and are used to shorten and clarify mathematical notation. As a result, if you wanted to multiple 10 by itself eight times, you could simply use an exponent to write 10 to the 8th power instead of 10x10x10x10x10x10x10x10. Exponents were not, however, always used in mathematics. The symbols of exponents and the related area of scientific notation instead developed over time.

Features
Modern exponential notation requires a main number, a variable (like x) or an integer (like eight), is followed by a raised number to indicate the exponent. The exponent indicates the number of times that the main number is multiplied by itself. Negative exponents indicate that the result is 1 divided by the number raised to the exponents power. Fractional exponents mean you should take the root of the main number.

Identification
The basic concept of exponents goes back at least as far as the ancient Greeks, with the mathematician Euclid using the term "power" to indicate the number of times that a number should be multiplied by itself. A 14th century scholar, Nicole Oresme, wrote numbers to indicate the use of powers in this sense. However, none of these early instances of the concept used symbolic notation to express the mathematics.

History
The use of raised numbers to indicate exponents dates to the 17th century. Herigonus used symbols such as a3 to indicate a times a times a, although he did not raise the exponent. The first raised exponents were used by David Hume in 1636, where he used raised roman numerals (like iii or ix) to show exponents. In 1637, Rene Descartes used positive exponents written in the modern way.

Types
The earliest uses of exponential notation were invariably for positive exponents. Isaac Newton was the first to use modern notation for a negative exponent in 1676. Fractional exponents were used without modern notation by Nicole Oresme in the 14th century, but they did not appear in the modern form until Newton in 1676.

Function
Exponents and their use in scientific notation were limited until the 19th century. At that time, it became standard to write larger numbers in scientific notation. As a result, numbers such as 8,900,000,000 became 8.9 time 10 to the power of 9. This increased use was a direct result of studies into astronomy and microscopy that required extremely large or small numbers.