What is a Base?

Base Definition

In a power, the base is the large number underneath the exponent. When you simplify the power, you will this number by itself multiple times (as determined by the exponent). 

For example, \(3^{2}\) means that you should multiply 3 by itself two times. 


Base of a Logarithm

In a logarithm, the base is the small number written in a subscript immediately after the log function. 

Logarithms allow us to find the missing exponent in a power. They can be written in exponential form as explained on this page. The exponential form of the logarithm above is...

Logarithmic Form


Exponential Form


The answer to this logarithm would be 4 because \(3^{4}=81\). The base of the logarithm is the same as the base of the power when the logarithm is written in exponential form. 

How to Simplify Negative Bases


When you have a negative base with an exponent, you simplify the power 

Positive Exponent with a Negative Base


Because we have a positive 3 in the exponent, we will multiply -4 by itself 3 times.

\((-4)^{3}= (-4)(-4)(-4)\)

Three negatives multiplied together is a negative.


Negative Exponent with a Negative Base





Fraction Exponent with a Negative Base




How to Simplify Fraction Bases



How to Simplify Decimal Bases



How to Simplify Advanced Bases


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Complex Numbers

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Free Printable Worksheets

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Free Online Practice Problems

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