Vocabulary BaseExponent Scientific Notation

Objective 1 You will be able to simplify expressions with numbers and variables using properties of exponents

Warm-Up, 1 Multiplication is simply repeated addition

Warm-Up, 2 An exponent is simply repeated multiplication

Exponents 2 3 = 2  2  2 Base Exponent Exponents mean repeated multiplication

Exercise 1

Investigation 1 In this Investigation, we will (re)discover some general properties of exponents. They include the Multiplication and Division Properties, and Power Properties.

Investigation 1: Multiplication Step 1: Rewrite each product in expanded form, and then rewrite it in exponential form with a single base. Step 2: Compare your answers to the original product. Is there a shortcut? Step 3: Generalize your observations by filling in the blank: b m ·b n = b -?- 3 4 · ·10 6 x3·x5x3·x5 a2·a4a2·a4

Investigation 1: Powers Step 1: Rewrite each expression without parentheses. Step 2: Generalize your observations by filling in the blanks: ( b m ) n = b -?- ( ab ) n = a -?- b -?- (4 5 ) 2 (x3)4(x3)4 (5 m ) n ( xy ) 3

Investigation 1: Division Step 1: Write the numerator and denominator in expanded form, and then reduce to eliminate common factors. Rewrite the factors that remain with exponents. Step 2: Generalize your observations by filling in the blank:

Properties of Exponents Multiplication Property of Exponents Division Property of Exponents Power Property of Exponents

Exercise 2 Practice simplifying expressions.

Exercise 3

Not the Power Property The Power Property of Exponents only works across multiplication and division NOT addition or subtraction!

Exercise 4 Evaluate the expression.

Exercise 5 Use the division property of exponents to rewrite each expression with a single exponent. Then expand each original expression and simplify. Compare your answers.

Properties of Exponents Zero Exponents Negative Exponents

Exercise 6 Simplify the expression.

Always Look on the Bright Side of Life… When you simplify an algebraic expression involving exponents, all the exponents must be POSITIVE. Negative exponents in the numerator need to go in the denominator

Always Look on the Bright Side of Life… When you simplify an algebraic expression involving exponents, all the exponents must be POSITIVE. Negative exponents in the denominator need to go in the numerator

Exercise 7a Simplify the expression.

Exercise 7b

Exercise 8 The radius of Jupiter is about 11 times greater than the radius of earth. How many times as great as Earth’s volume is Jupiter’s volume?

Exercise 9

Exercise 10

Scientific Notation Easy to multiply, divide, and raise to powers using the properties of exponents NOT so easy to add and subtract

Exercise 11 Write the answer in scientific notation.

5.1: Use Properties of Exponents Objectives: 1.To simplify numeric and algebraic expressions using the properties of exponents Insert your face here