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How do I use properties of exponents to simplify expressions involving powers?

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4.1 Use Properties of Exponents Properties of Exponents Let a and b be real numbers and let m and n be integers. Product of Powers Property Power of a Powers Property Power of a Product Property Negative Exponents Property Zero Exponent Property Quotient of Powers Property Power of a Quotient Property

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4.1 Use Properties of Exponents Example 1 Evaluate a numerical expression

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4.1 Use Properties of Exponents Checkpoint. Evaluate or simplify the expression.

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4.1 Use Properties of Exponents Example 2 Use scientific notation in real life Iceland covers about 1.03 X 10 5 square kilometers and has a population of approximately 2.94 X 10 5 people. About how many people are there per square kilometer? Solution Divide population by land area. Quotient of powers property Use a calculator Zero exponent property There are about ___ people per square kilometer.

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4.1 Use Properties of Exponents Example 3 Simplify expressions Power of a product property Power of a power property Quotient of powers property Simplify exponents Zero exponent property Negative exponent property

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4.1 Use Properties of Exponents Example 3 Simplify expressions Power of a quotient property Power of a power property Negative exponent property

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4.1 Use Properties of Exponents Checkpoint. Simplify or evaluate the expression. Tell which properties of exponents you used. Product of powers property

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4.1 Use Properties of Exponents Checkpoint. Simplify or evaluate the expression. Tell which properties of exponents you used. Power of a quotient/product property Power of a power property Quotient of powers property

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4.1 Use Properties of Exponents Example 4 Compare real-life volumes Beach Ball The radius of a beach ball is about 5.6 times greater than the radius of a baseball. How many times as great as the baseball’s volume is the beach ball’s volume? Let r represent the radius of the baseball The volume of a sphere is Power of a Product property property

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4.1 Use Properties of Exponents Example 4 Compare real-life volumes Beach Ball The radius of a beach ball is about 5.6 times greater than the radius of a baseball. How many times as great as the baseball’s volume is the beach ball’s volume? Let r represent the radius of the baseball Quotient of Powers Zero Exponent Property Approximate power The beach ball’s volume is about ____ times as great as the baseball’s volume.

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4.1 Use Properties of Exponents Checkpoint. Complete the following exercise. 4.Rework Example 4 where the radius of a beach ball is about 6 times the radius of a baseball. 216 times as great

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4.1 Use Properties of Exponents Pg. 117, 4.1 #1-42

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EXAMPLE 1 Evaluate numerical expressions a. (– 4 2 5 ) 2 = 16 2 5 2 Power of a product property Power of a power property Simplify and evaluate power.

EXAMPLE 1 Evaluate numerical expressions a. (– 4 2 5 ) 2 = 16 2 5 2 Power of a product property Power of a power property Simplify and evaluate power.

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