Types of Exponents
In this lesson, we will give a short summary of exponents: positive exponents, zero exponents, negative exponents, fractional exponents, adding exponents and multiplying exponents.
The following diagram shows the types of exponents: positive exponents, negative exponents, rational exponents, and zero exponents. Scroll down the page for more examples and solutions for the types of exponents.
Positive Exponents
Exponents are a shorthand way to show how many times a number, called the base, is multiplied to itself. A number with an exponent is said to be “raised to the power” of that exponent.
Example:
Two raised to the power of three = 23 = 2 × 2 × 2 = 8
Any number raised to the power of one equals itself, for example:
151 = 15
Zero Exponents
Any number (except 0) raised to the zero power equals 1, for example:
3220= 1
Negative Exponents
A negative exponent means that the base is changed to its reciprocal and then raised to the power of the positive exponent, for example:
5-3 = 
54 x 5-3 = 54-3 = 5
The following video show more examples of negative exponents:
Fractional Exponent
A fractional exponent in the form of 
means to take the nth root of the base, for example:
is the square root of 4.
The following video show more examples of fractional exponents:
Adding Exponents
If two numbers with exponents have the same base, you can multiply them by adding the exponents, for example:
4510 × 4531 = 4541
Multiplying Exponents
When you have a power of a power, you multiply the exponents, for example:
The Rules Of Exponents
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