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+ Using Properties of Exponents EQ: How do we use properties of exponents? M2 Unit 5a: Day 1 Wednesday, October 07, 2015

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

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+ Product of Powers: Examples: a. b. To multiply powers with the same base, add the exponents and keep the common base.

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+ Your turn: 1. 2. 3. Keep common bases Add the exponents

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+ Power of a Power: Examples: a. b. To raise a power to a power, keep the base and multiply the exponents.

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+ Your turn: 1. 2. 3. Keep The Base Multiply The Exponents

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+ Power of a Product: Examples: a. b. To raise a product to a power, raise each factor to the power. This should remind you of the distributive property. Remember to “distribute” the exponent to each base, numeric and variable! Warning: No distributing over addition!!! Simplify any numeric bases raised to exponents

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+ Your turn: 1. 2. 3. Raise Each Factor To The Power It’s Like The Distributive Property

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+ Zero Exponent: Examples: a. b. Any number raised to the zero power is equal to “1”.

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+ Your turn: 1. 2. 3. Anything Raised To The Zero Power =1

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+ Quotient of Powers: Examples: a. b. To divide powers with the same base, subtract the exponents and keep the common base. Also, remember that common factors cancel out! Keep the base where the exponent is larger

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+ Your turn: 1. 2. 3. Common Factors Cancel Out With Common Bases Subtract Exponents

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+ Power of Quotient: Examples: a. b. To raise a quotient to a power, raise the numerator and the denominator to the power.

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+ Your turn: 1. 2. 3. Raise the numerator and denominator to the power Simplify any factors with numeric bases

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+ You may want to think of it this way: unhappy ( ) exponents will become happy ( ) by having the base/exponent pair “switch floors”! Example: A.) B.) Negative Exponent Property:

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+ You try: 1. 2. 3. 4.

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+ Simplifying Exponential Expressions To simplify exponential expressions completely: Get rid of parentheses Get rid of negative exponents Make sure there is only one of each base Cancel out common factors

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+ Simplify the exponential expression. Examples: A. B. D. multistep C.

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+ 1. 2. 3. 4. You try: multistep

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+ Simplify the exponential expression. A. B. C. D. multistep

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+ You Try: 5. 6. 7. multistep

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