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DISTRIBUTIVE PROPERTY AND POWER PROPERTIES You Control the Power!

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Distributive Property Distribute a monomial over any polynomial: Example: 2x( 5x 3 + 7x 2 - 3x) = ? Answer: 10x 4 + 14x 3 - 6x 2 Next slide: What if the first term is a binomial? Then repeat the process!

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Distributive Property If the first expression has more than one term simply distribute each term through the entire second parentheses and then combine like terms: Example: (2x – 6)( 5x 3 + 7x 2 - 3x) = ? Answer: 10x 4 + 14x 3 - 6x 2 - 30x 3 - 42x 2 + 18x 10x 4 - 16x 3 - 48x 2 + 18x

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Distributive Property You try this one. Click to check your answer. Example: (6a – 5)( 2a 3 - 3a 2 - a) = ? Answer: 12a 4 – 18a 3 – 6a 2 – 10a 3 + 15a 2 + 5a 12a 4 – 28a 3 + 9a 2 + 5a

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Product of Powers Property When multiplying terms with the same base add the exponents Example: x 3 x 5 = x 8 When in doubt, stretch it out: x 3 x 5 xxx xxxxx

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Quotient of Powers Property When dividing powers with the same base subtract the exponents (This has the same effect as cancelling.) Example: When in doubt, stretch it out:

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Power of a Power Property When applying an exponent to an exponent multiply the exponents Example: ( x 3 ) 5 = x 15 When in doubt, stretch it out: ( x 3 ) 5 ( x 3 ) ( x 3 ) ( x 3 ) ( x 3 ) ( x 3 ) xxx xxx xxx xxx xxx

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Power of a Product Property When an exponent is applied outside a parenthetical product, it applies to each factor individually (Be careful not to call this distributive!) Example: When in doubt, stretch it out:

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Power of a Quotient Property When an exponent is applied outside a quotient, it applies to each part individually Example: When in doubt, stretch it out:

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Zero Power Property Any non-zero base to the zero power is equal to 1 Examples: x 0 = 1 or 56 0 = 1 Why should this be true? Quotient of Powers Property is one easy explanation.

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Zero Product Property If two factors have a product of zero, then one of those factors must equal zero. Example: If xy = 0, then x = 0 or y = 0. Why should this be true? How can you multiply two numbers and get zero for an answer?

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Negative Power Property A negative power in the numerator, gets moved to the denominator. Examples: Why should this be true? Quotient of Powers Property is one easy explanation.

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Self Check: find the answer and name the property you used. -hit any key to reveal the answer by the Product of Powers Property

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Self Check: find the answer and name the property you used. -hit any key to reveal the answer by the Power of a Power Property

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Self Check: find the answer and name the property you used. -hit any key to reveal the answer by the Quotient of Powers Property

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Self Check: find the answer and name the property you used. -hit any key to reveal the answer by the Negative Power Property

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Self Check: find the answer and name the property you used. -hit any key to reveal the answer =1 by the Zero Power Property

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Self Check: find the answer and name the property you used. -hit any key to reveal the answer 3x = 0 or x – 1= 0 by the Zero Product Property If (3x)(x – 1) = 0, then

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