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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

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[edit | edit source]

Exponentiation Resources
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