Algebra 1 Properties of Exponents Notes...
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Page 1 Properties of Exponents Notes 6.1 Using Zero & Negative Exponents Zero Exponent—For any nonzero a, _________. The power of __________________. Examples: Negative Exponents—For any integer n, and any nonzero number a, __________is the ______________ of ________. Examples: Example 1: Using Zero & Negative Exponents Evaluate each expression. a.) 6.7 ! b.) (−2) !! Example 2: Simplifying an Expression Simplify the expression !! ! ! !! You Try! Evaluate the expression. 1. (−9) ! 2. 3 !! 3. !! ! ! !! 4. Simplify the expression ! !! ! !! ! ! . Write your answer using only positive exponents. Using Properties of Exponents Product of Powers Property—Let a be a real number, and let m and n be integers. To ____________ powers with the same ___________, ___________ their exponents. ______ ⋅ _______ = __________ Example: Quotient of Powers Property—Let a be a nonzero real number, and let m and n be integers. To ____________ powers with the same ___________, _______________ their exponents. ______ ⋅ _______ = __________ where a _____ 0 Example: Power of a Power Property—Let a be a real number, and let m and n be integers. To find a ______________ of a power, _______________ their exponents. (_______) _____ = __________ Example: Example 3: Using Properties of Exponents Simplify each expression. a.) 3 ! ∙ 3 ! b.) !! ! !! ! c.) ! !! You Try! Simplify the expression. Algebra 1
Transcript of Algebra 1 Properties of Exponents Notes...
Page 1
Properties of Exponents Notes 6.1
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Zero Exponent—For any nonzero a, _________. The power of __________________. Examples:
Negative Exponents—For any integer n, and any nonzero number a, __________is the ______________ of ________. Examples:
Example 1: Using Zero & Negative Exponents Evaluate each expression. a.) 6.7! b.) (−2)!!
Example 2: Simplifying an Expression Simplify the expression !!
!
!!!
You Try! Evaluate the expression. 1. (−9)! 2. 3!! 3. !!
!
!!!
4. Simplify the expression !
!!!!!
!!. Write your answer using only positive exponents.
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Product of Powers Property—Let a be a real number, and let m and n be integers. To ____________ powers with the same ___________, ___________ their exponents.
______ ⋅ _______ = __________ Example:
Quotient of Powers Property—Let a be a nonzero real number, and let m and n be integers. To ____________ powers with the same ___________, _______________ their exponents.
______ ⋅ _______ = __________ where a _____ 0
Example:
Power of a Power Property—Let a be a real number, and let m and n be integers. To find a ______________ of a power, _______________ their exponents.
(_______)_____ = __________ Example:
Example 3: Using Properties of Exponents Simplify each expression. a.) 3! ∙ 3! b.) !!
!
!! ! c.) 𝑧! !!
You Try! Simplify the expression.
Algebra 1
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Properties of Exponents Notes 6.1
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Product of a Product Property—Let a be a real number, and let m be integers. To find a ____________ of a ______________, find the _____________ of each _______________ and _________________.
(__________)_____ = __________ Example:
Power of a Quotient Property—Let a be a real number with 𝑏 ≠ 0, and let m be an integer. To find the ______________ of a _______________, find the power of the ________________ and the power of the __________________ and _____________.
(_______)_____ = __________ where 𝑏 ≠ 0
Example:
Example 3: Using Properties of Exponents Simplify each expression.
You Try! Simplify the expression.
Algebra 1
