What are exponential function rules?

Exponential function rules are the mathematical guidelines for functions that take the form of f(x) = b^x, where the base is a positive real number. With these functions, the growth rate is proportional to their value.

While there are many rules that govern exponential functions, there are several main rules used to dictate specific functions. One unique exponential function is e^x, where the growth rate of this function at x is exactly e^x. Another unique relationship occurs when any exponential function takes the form b^0. This function is always equal to one, provided that the value of b is not equal to zero.

Other rules are more general. For exponential functions that take the form b^x+y, their value is equal to (b^x)(b^y). For functions of the form b^xy, their value is equal to (b^x)^y. Similar to this rule, functions that take the form ba^x are equal to (b^x)(a^x). Additionally, functions that take the form b^-x are equal to 1/(b^x).

It should also be noted that square root functions are a special type of exponential function. These functions of the form f(x) = sqrt(x) are equal to x^1/2. The same can be said for cubic root and other functions that take a similar form.