What Are Indices in Mathematics?

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Indices are a mathematical concept for expressing very large numbers. They are also known as powers or exponents. In the mathematical process of exponentiation, a base number is written alongside a superscript number, which is the index or exponent.

Indices explain how many copies of the base number are multiplied. For instance, a base to the second power is referred to as the base squared and indicates that the base is multiplied by itself once. A base with an index of 3 is referred to as base cubed. Exponential phrases are often stated as a number to the power of its index. For instance, 3 to the 5th power.

The process of exponentiation is governed by a set of rules known as the laws of indices, or exponent laws. The rules include the concept that any number other than 0 is always equal to 1 if its index or exponent is 0. Another rule holds that to divide mathematical expressions that have the same base, it is necessary to copy the base and subtract the exponents.

Exponentiation is used in many areas of study besides math, including chemistry, computer science, physics and biology. It is also used in practical applications, such as calculating compound interest and predicting an increase in population. French mathematician Rene Descartes created the method for notating exponents in 1637.