Power (mathematics)

Power (mathematics), term used to describe the result of repeatedly multiplying a number by itself. The number that is successively multiplied by itself is called the base. A small raised number called an exponent follows the base and indicates the number of times the base is to be multiplied. For example, 2³ equals 2 × 2 × 2, and 4⁵ = 4 × 4 × 4 × 4 × 4.

Together, a base and an exponent form an exponential expression. When an exponential expression is written, the base is said to be raised to the power of the exponent. 'Ten raised to the fourth power,' for example, would be 10⁴ or 10,000. This phrase can be shortened to 'ten to the fourth power' or even 'ten to the fourth.' A number raised to the second power is sometimes called squared, while a number raised to the third power may be called cubed. The word power sometimes also means the exponent alone rather than the result of an exponential expression.

Bases and exponents can be variables or more complicated algebraic expressions, such as (x + y), as well as simple numbers. For example, mⁿ means the quantity m raised to the nth power, and (x + y)² means (x + y)(x + y), or x² + 2xy + y². See Root.