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» » Laws of Exponents

Using the Laws of Exponents


Before you begin working with monomials and polynomials, you will need to understand the laws of exponents. There are three laws or properties that I am going to discuss in this lesson.



We will look at the following properties:

  • Multiplying Powers with the Same Base

  • Power of a Power Property

  • Power of a Product Property


For each of the three laws, we will write a few examples in expanded form. This will help you to understand why the law works. The I will define the property. Finally we will look at a few examples.



Ok... let's get started!



Multiplying Powers with the Same Base


laws of exponents



Tip

When a term does not contain an exponent, it is assumed to be 1.

For example:

3 = 31        y = y1        r = r1



Power of a Power Property


power or a power property for laws of exponents



I know that these properties can be confusing. If you need direct video instruction, check out the Algebra Class E-course.



Power of a Product Property


Before we start this one, let's define the word product.

A product is the answer to a multiplication problem.

So, power of a product means that we are raising a multiplication problem to a power. Take a look at this example:

power of a product property




Those are the only three properties that you'll need to remember for this unit! As you complete the practice problems below, refer back to the properties if needed!




Practice Problems


Directions: For each problem identify the property used. Then simplify to lowest terms.

laws of exponents practice





Answer Key


laws of exponents answers



Great Job! Now let's move onto learning about monomials!



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