## The Exponent Calculator Formula

$y = x^{n}$

## Definition of the Exponent Function

The function f(x) = a^x can be defined for various types of numbers, including integers, rational numbers, real numbers, and even complex numbers. The value of "x" can be positive, negative, or zero.When "x" is a positive integer, the exponent function represents the repeated multiplication of the base "a" by itself "x" number of times. For example, if a = 2 and x = 3, then 2^3 = 2 × 2 × 2 = 8.When "x" is a negative integer, the exponent function involves taking the reciprocal of the base raised to the positive value of "x." For example, if a = 2 and x = -2, then 2^-2 = 1 / (2 × 2) = 1 / 4 = 0.25.When "x" is a fraction or a decimal, the exponent function extends the concept of repeated multiplication to include non-integer exponents. The exact calculation depends on the specific values of "a" and "x." For example, if a = 2 and x = 1.5, then 2^1.5 ≈ 2.8284.The exponent function has various important properties, such as the laws of exponents, which govern how exponents interact with each other during mathematical operations like addition, subtraction, multiplication, and division.