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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

### Zero Exponents

### Negative Exponents

### Fractional Exponent

### Adding Exponents

### Multiplying Exponents

The Rules Of Exponents

More Lessons for Arithmetic

Math Worksheets

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.

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 = 2

^{3}= 2 × 2 × 2 = 8

Any number raised to the power of one equals itself, for example:

15

^{1}= 15

Any number (except 0) raised to the zero power equals 1, for example:

322

^{0}= 1

A **negative
exponent** means that the base is changed to its reciprocal and then raised to
the power of the positive exponent, for example:

The following video show more examples of negative exponents:5

^{-3}=

5

^{4}x 5^{-3}= 5^{4-3}= 5

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:

If two numbers with exponents have the same base, you can multiply them by adding the exponents, for example:

45

^{10}× 45^{31}= 45^{41}

When you have a **power of a power**, you multiply the exponents, for example:

The Rules Of Exponents

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