Exponentiation

Exponentiation is an operation involving two numbers, the base b and the exponent or power n. It is written as bⁿ using a superscript, or as b^n using the caret sign (^). The name is derived from the Latin word exponere, meaning "to put outside".

When n is a whole number, exponentiation corresponds to repeated multiplication of the base:

3² = 3 × 3 = 9
2³ = 2 × 2 × 2 = 8

Note that 3² ≠ 2³. There are, therefore, two different inverse (opposite) operations of exponentiation: taking the root and taking the logarithm.

History

Already the Greek scholar Archimedes of Syracuse (about 287 BC – about 212 BC) and the Persian astronomer and mathematician Muhammed ibn Musa al-Khwarizmi (about 780 – about 850) were familiar with the concept of exponentiation. The word exponent was coined in 1544 by the German monk and mathematician Michael Stifel (1487 – 1567).

Related concepts

• addition
• arithmetic
• division
• logarithm taking
• multiplication
• number
• numeral
• root taking
• subtraction