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

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

4.1 Use Properties of Exponents Example 1 Evaluate a numerical expression

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

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.

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

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

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

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

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

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.

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

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