Presentation on theme: "Vocabulary BaseExponent Scientific Notation. Objective 1 You will be able to simplify expressions with numbers and variables using properties of exponents."— Presentation transcript:
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 ·3 2 10 3 ·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
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