Exponentiation

Exponentiation is a mathematical operation, written as b^n, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b^n is the product of multiplying n bases:

b^n = b × b × ... × b n factors.

Definition

Exponentiation is a mathematical operation, written as b^n, involving two numbers, the base b and the exponent n. When n is a positive integer, exponentiation corresponds to repeated multiplication of the base: that is, b^n is the product of multiplying n bases:

b^n = b × b × ... × b n factors.

Properties

Exponentiation has properties that it shares with other operations on numbers. Some of these properties are:

• b^0 = 1 for any b (except b = 0), because any number except 0 raised to the power of 0 is 1.
• b^1 = b for any b, because any number raised to the power of 1 is the number itself.
• b^n = b × b^n−1 for any b and any positive integer n, because any number raised to a power is that number times the number raised to one less than that power.

Applications

Exponentiation is used in a wide variety of contexts, including in algebra, calculus, geometry, and computer science. It is also used in practical applications such as calculating interest rates, population growth, and radioactive decay.

See also

• Multiplication
• Division
• Addition
• Subtraction

• Exponentiation
  Exponentiation
• Odd powers of a number
  Odd powers of a number
• Even powers of a number
  Even powers of a number
• Roots of a number
  Roots of a number
• Continuity of the exponential function at 0
  Continuity of the exponential function at 0
• Cube root of one
  Cube root of one