Question

what are exponents and please provide examples

Answer 1

Exponentiation is a mathematical operation, written as b^n, involving two numbers, the base b and the exponent (or index or power) n. When n is a positive integer, exponentiation corresponds to repeated multiplication; in other words, a product of n factors, each of which is equal to b (the product itself can also be called power):

b^n = b*b*...*b (n times).

Example: 2^8 = 2*2*2*2*2*2*2*2 = 256.

The function e^x is called the exponential function, where e is the number (approximately 2.718281828) such that the function e^x is its own derivative. The exponential function is used to model a relationship in which a constant change in the independent variable gives the same proportional change (i.e. percentage increase or decrease) in the dependent variable. The function is often written as exp(x).

Example: e² ≈ 2.718281828² = 7.389056096435021584.