Lesson 1: Properties of Exponents

Objective: Simplify expressions using the properties of exponents.

Exponential notation indicates repeated multiplication of the same number. The exponent indicates how many times the base is used as a factor. In the example of exponential notation shown below, the base is 3 and the exponent is 4. This expression is read "three to the fourth power."

3⁴ = 3 x 3 x 3 x 3

Expressions containing exponents can be simplified using several properties of exponents; examples are shown in the videos below. The first video introduces two properties of exponents: the product rule and the quotient rule. The product rule is applied when multiplying exponential expressions having the same base, while the quotient rule is applied when dividing exponential expressions having the same base. Watch this video now.

The second video justifies the definition of the number zero as an exponent, and also explains the reasoning behind a property called the power rule, which is used when raising a power to another power. Watch this video now.

The third video demonstrates two more properties of exponents that are used when raising a product or a quotient to a power. Watch this video now.

A list containing all properties of exponents discussed in the above videos is shown below.

Complete the worksheet attachment below and then check your answers using the solutions attachment. Once you have completed these exercises, click the link to advance to the next lesson.