Bell Quiz

Objectives Simplify expressions containing integer and zero exponents.

Expressions with Exponents Algebraic expressions may contain exponents that are positive, negative, or zero. The relationship between the different exponents can be understood by looking at successive powers of a positive integer grater than 1.

Expressions with Exponents Look at the powers of 2 In the left column, each entry is found by decreasing the exponent in the previous entry by one. In the right column each entry is found by halving the pervious entry (or dividing by 2).

Expressions with Exponents What if we continued this pattern? The pattern illustrates the properties for negative and zero exponents.

Negative and Zero Exponent Properties An algebraic expression is not considered simplified if it contains negative or zero exponents. The Product Property of Exponents applies to negative and zero exponents.

Example 1 Simplifying Expressions with Negative Exponents Simplify the expression. All variables represent non-zero real numbers

Lesson Practice Simplify the expression

Example 2 Simplifying Expressions with Negative Exponents Simplify the expression. All variables represent non-zero real numbers

Lesson Practice Simplify the expression

Example 3 Simplifying Expressions with Negative Exponents Simplify the expression. All variables represent non-zero real numbers

Lesson Practice Simplify the expression

Example 4 Evaluating Expressions with Negative and Zero Exponents Evaluate the expression for a = – 2 and b = – 3 a 2 b 0

Lesson Practice Evaluate the expression for a = 4, b = 6 and c = 3 a 0 bc 2

Example 5 Evaluating Expressions with Negative and Zero Exponents Evaluate the expression for b = – 3 3b –3 ∙ b

Lesson Practice Evaluate the expression for a = 4 4a –2

Quotient Property of Exponents The Quotient Property of Exponents is used when dividing algebraic expressions. This property states that to divide two algebraic expressions with the same base, subtract their exponents.

Example 6 Using the Quotient Property of Exponents Simplify the expression. All variables represent non-zero real numbers

Lesson Practice Simplify the expression. All variables represent non-zero real numbers

Example 7 Using the Quotient Property of Exponents Simplify the expression. All variables represent non-zero real numbers

Lesson Practice Simplify the expression. All variables represent non-zero real numbers

Example 8 Using the Quotient Property of Exponents Simplify the expression. All variables represent non-zero real numbers

Lesson Practice Simplify the expression. All variables represent non-zero real numbers

Example 9 Application: the Intensity of Sound The intensity of sound can be measured in watts per square meters. The table below lists intensity levels for some common sounds How many times more intense is the sound of a rocket liftoff than that of regular speech?

Lesson Practice How many times more intense is the sound of a jet liftoff than that of a vacuum cleaner? Express the answer in exponential and standard form.