How do I use properties of exponents to

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

4. 1 Use Properties of Exponents Let a and b be real numbers and let m and n be integers. Product of 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 105 square kilometers and has a population of approximately 2. 94 X 105 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 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

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