Pre-Algebra Q1W8: Properties of Exponents. Objectives I know my perfect squares up to 15. I know the properties of exponents, including : The “zero power”

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Presentation transcript:

Pre-Algebra Q1W8: Properties of Exponents

Objectives I know my perfect squares up to 15. I know the properties of exponents, including : The “zero power” property Multiplying (“product”) Property Dividing (“quotient”) Property Power of a Power Property

Exponents The exponent of a number tells you how many times to use the number in a multiplication:

“Squared” versus “Square Root”

Exponents Exponents make it easier to write and use many multiplications:

“Perfect Squares” A “perfect square” is a number made by squaring a whole number.

Perfect Squares Please memorize your Perfect Squares up to 15.

Laws of Exponents: These 2 cases are VERY IMPORTANT to know:

Laws of Exponents: Write these in your notebook and solve: (8 1 ) = (5 1 ) = (7 0 ) = (5 0 ) = (4 1 ) = (2 0 ) =

Laws of Exponents: Multiplication When you multiply terms with the same base, you can add the exponents: Example: (3 2) x (3 3 ) = 3 5 Check: 9 x 27 = = 3 x 3 x 3 x 3 x 3 = 243

Laws of Exponents: Multiplication Example: Simplify: (2 2 ) x (2 3 ) = = 4 and 2 3 = 8 4 x 8 = 32 2 x 2 x 2 x 2 x 2 = 32 (5 2 ) x (5 1 ) = (6 4 ) x (6 -2 ) = (4 2 ) x (4 -1 ) =

Laws of Exponents: Multiplication Simplify (7 3 ) x (7 2 ) = (2 2 ) x (2 3 ) = (4 5 ) x (4 4 ) =

Laws of Exponents: Division When you divide terms with the same base, you can subtract the exponents:

Laws of Exponents: Division It’s important for you to remember that division can be expressed in two ways:

Laws of Exponents: Division Let’s Try It: You Try It: Check: Let’s do one together: (4 3 ) ÷ (4 2 ) = (6 4 ) ÷ (6 2 ) = (5 8 ) ÷ (5 4 ) =

Laws of Exponents: Power to a Power When you raise a power to a power, multiply the powers. Example: (5 3 ) 4 = (5 3 )(5 3 )(5 3 )(5 3 ) = 5 12 Or, we can say 5 3x4 = 5 12 : Just multiply the powers!

Laws of Exponents: Power to a Power Practice (5 2 ) 6 = (8 3 ) 4 = (7 4 ) 5 =

Objectives Review/Closure I know my perfect squares up to 15. I know the properties of exponents, including : The “zero power” property Multiplying (“product”) Property Dividing (“quotient”) Property Power of a Power Property