Decimal Places of Irrational Numbers | Calculate with Large Numbers | Billion and Milliard | Write Out Powers | Exponential Function

Exponential Function: Calculate Powers

Calculates very large and very small numbers that can occur quickly in power calculations An exponential function has the term y=a^x. The function y=n*a^x can be used here. n is the factor by which the subsequent power is multiplied, a is the base by which the multiplication is done and x is the exponent, i.e. how many times the multiplication is done.
Places before decimal point indicate which numbers are written out as the result and from when the e-notation is used.

Places before decimal point:
Factor n:
Base a:
Exponent x:

Result:

The exponent x must be an integer, which can also be negative. The factor n and the base a can be any number. A frequently used base is Euler's number e, so e can also be entered for the base.

Example: with a factor of 2, a base of 10, and an exponent of 5, the result is 200000, written out as two hundred thousand. Ten to the power of five is a one with five zeros, which is hundred thousand. Multiplying this by two gives the result.

A calculation like a to the power of b is called a power. If you want to create a corresponding function from such a calculation, there are two possibilities. Let the function variable be x, a and b are constants. Then x to the power of b is a power function and a to the power of x is an exponential function. Exponential functions grow faster than power functions; this growth is called exponential growth, a term that is often heard outside of pure mathematics. With exponential growth, extremely high values are quickly reached; if a process is described in reality with this type of growth, it quickly reaches its natural limits. For example, cell division is a process with exponential growth with a base of 2; one cell becomes 2, 2 becomes 4, 4 becomes 8, and so on. At some point this stops, either because the target size is reached, or because there is no more space, or because the cells die faster than new ones are formed due to changing environmental conditions.

Last updated on 08/20/2025. Author: Jürgen Kummer

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