# Types of Exponents

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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

### 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.

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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