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Properties of Exponents
August 27th, 2013
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Exponential Expressions in Expanded Form
Write Each Expression in expanded form (4π¦) 3 (4π¦)(4π¦)(4π¦) βπ 2 -(a β a) = -πβπ 2 π¦ 2 ( π₯β3) 3 2 π¦ π¦ π₯β3 π₯β3 (π₯β3) The base is 4y, and the exponent is 3. 4y is a factor 3 times.
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Product of Powers Property
When multiplying two of the same bases, add the exponents. 4 2 β 4 3 = 4 5 16 β 64 = 1024 4 5 = 1024 π₯ 6 β π₯ 2 = π₯ 8 (x β x β x β x β x β x) β (x β x)
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Power to a Power Property
When you have a power raided to another power, multiply the exponents. = 4 6 4 2 β 4 2 β 4 2 π₯ = π₯ 15 π₯ 3 β π₯ 3 β π₯ 3 β π₯ 3 β π₯ 3
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Power of a Product Property
You can βdistributeβ an exponent to other exponents. π₯ 2 π¦ = π₯ 6 π¦ 4 5 π₯ 2 π¦ = 25 π₯ 4 π¦ 6
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Try theseβ¦ π₯ 3 β π₯ 8 π₯ 5 βπ₯β π₯ 2 π¦ 2 β π¦ β8 β π¦ 11 π 5 4 π 7 0
π 5 4 π 7 0 6π₯ π¦ 4 3
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Multi-step Problems π β π 5 3 4 π₯ β 5π₯ 3 β2π₯ 3 β π₯ 4 β2
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Quotient of Powers Property
When dividing two of the same bases, subtract the exponents. 3β3β3β3β3 3β3 3 3 =27 π₯ 8 π₯ 3 π₯βπ₯βπ₯βπ₯βπ₯βπ₯βπ₯βπ₯ π₯βπ₯βπ₯ π₯ 5
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Power of a Quotient Property
You can βdistributeβ an exponent to all the other exponents in a fraction. 9 16 π₯ 5 π¦ π₯ 20 π¦ 12
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Negative Power of a Quotient Property
If a fraction is raised to a negative exponent, flip the fraction and make the exponent positive. 2 5 β3 = π₯ 4 π¦ 7 β2 π¦ 7 π₯ π¦ 14 π₯ 8
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Try theseβ¦ π₯ 8 π₯ 6 π₯ 7 π₯ 10 π₯ 5 π₯ 9 π₯ 4 π¦ 3 π₯ 5 π¦ 2 3 2 π₯ 4 π¦ 2 3
π₯ 8 π₯ 6 π₯ 7 π₯ 10 π₯ 5 π₯ 9 π₯ 4 π¦ 3 π₯ 5 π¦ 2 π₯ 4 π¦ π₯ 2 π¦ 6 β5
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