Chapter 7: Exponential Chapter 7: Exponential FunctionsFunctions7.1 & 7.2Laws of ExponentsZero and Negative Exponents

The Product RuleThe Product Rule

When multiplying exponential expressions with the same base, add the exponents.

Multiply each expression using Multiply each expression using the product rulethe product rule

Multiply each expression using Multiply each expression using the product rulethe product rule

4 3 26 5x y x y

Multiply each expression using Multiply each expression using the product rulethe product rule

3 4 2 64 10x y x y

The Quotient RuleThe Quotient Rule

When dividing exponential expressions with the same non-zero base, subtract the exponents.

Divide each expression using Divide each expression using the quotient rulethe quotient rule

7

4

2

2

Divide each expression using Divide each expression using the quotient rulethe quotient rule

12 9

3 7

30

5

x y

x y

Divide each expression using Divide each expression using the quotient rulethe quotient rule

14 8

3 5

27

3

x y

x y

Zero as an exponentZero as an exponent

Any real number (other than zero) raised to the zero power is 1.

The Negative-Exponent The Negative-Exponent RuleRule

Use the negative-exponent rule to Use the negative-exponent rule to write each expression with a write each expression with a positive exponent.positive exponent.

29

Use the negative-exponent rule to Use the negative-exponent rule to write each expression with a write each expression with a positive exponent.positive exponent.

5 27x y

Use the negative-exponent rule to Use the negative-exponent rule to write each expression with a write each expression with a positive exponent.positive exponent.

2

1

6

The Power Rule (Powers to The Power Rule (Powers to Powers)Powers)

When an exponential expression is raised to a power, multiply the exponents.

Simplify each expression using Simplify each expression using the power rulethe power rule

322

Simplify each expression using Simplify each expression using the power rulethe power rule

35y

Simplify each expression using Simplify each expression using the power rulethe power rule

42b

Products to PowersProducts to Powers

When a product is raised to a power, raise each factor to that power.

SimplifySimplify

322x

SimplifySimplify

533xy

Quotients to PowersQuotients to Powers

When a quotient is raised to a power, raise the numerator and denominator to that power, divide to simplify if necessary

SimplifySimplify4

3

x

SimplifySimplify32

4

x

Simplifying Exponential Simplifying Exponential ExpressionsExpressions

An exponential expression is ___________ when:◦No parenthesis appear◦No powers are raised to powers◦Each base occurs only once◦No negative or zero exponents appear

Note: Simplify in this order!

SimplifySimplify

34 53x y

SimplifySimplify

4 5 67 2xy x y

SimplifySimplify2 4

6 8

35

5

x y

x y

SimplifySimplify324x

y

HomeworkHomeworkExercise Set P.3 #1 – 63 odd