what is the mathmatical definition of exponent
In mathematics, an exponent is a value that indicates the number of times a base number is multiplied by itself. It is written as a superscript to the right of the base number.
The mathematical definition of an exponent is as follows:
For a base number a and an exponent n, where n is a positive integer:
- The exponentiation of a to the power of n, denoted as an, is the result of multiplying a by itself n times.
- For example, a^3 means a × a × a.
Exponents can also be negative, fractional, or zero:
- A negative exponent indicates the reciprocal of the base raised to the positive power. For example, a^(-n) = 1 / (a^n).
- A fractional exponent indicates the root of the base. For example, a^(1/n) = the nth root of a.
- A base raised to the power of zero, a^0, is defined as 1.
Note: Exponents follow certain rules and properties, such as the product rule, quotient rule, power rule, and many others, which govern how they interact with other mathematical operations.