Exponentiation is a binary operator that operates on a base and exponent value. The exponent operator is represented by writing the exponent value in superscript style. For discrete numbers, a base value to the power is the same as multiplying the base by itself times. For example, raised to the value is equal to multiplied by multiplied by as shown in the equation below.
The exponent operator models exponential growth and is related to the logarithm and radical operators. The relationship between the three operators and the nature of the exponent operator itself can be visualized by drawing a tree structure.
Shown below are examples that demonstrate the result of the exponent operator for discrete numbers.
The properties of the exponent operator are summarized in the table below. These properties can be used to manipulate math expressions into new forms.
The exponential operator is closely related to the logarithm and radical operators. For example, given the scenario of exponential population growth, the relationship between the three operators is expressed below. Note, in this hypothetical scenario the initial population is represented with the value of .
Given the growth rate and the time elapsed, the exponent operator returns the population.
Given the growth rate and the population the logarithm operator returns the time elapsed.
Given the time elapsed and the population the radical operator returns the growth rate.