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Published byLinette Cole Modified over 7 years ago

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Note: There are 56 problems in The HW 5.1 assignment, but most of them are very short. (This assignment will take most students less than an hour to complete.)

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Teachers: You can insert screen shots of any test problems you want to go over with your students here.

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Please CLOSE YOUR LAPTOPS, and turn off and put away your cell phones, and get out your note- taking materials.

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Section 5.1 Exponents

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Exponents that are natural numbers are shorthand notation for repeating factors. 3 4 = 3 3 3 3 3 is the base 4 is the exponent (also called power) Note, by the order of operations, exponents are calculated before all other operations, except expressions in parentheses or other grouping symbols.

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Product Rule (applies to common bases only) a m a n = a m+n Simplify each of the following expressions. Example 3 2 3 4 = 3 6 = 3 3 3 3 3 3= 729 x 4 x 5 = x 4+5 z 3 z 2 z 5 = z 3+2+5 (3y 2 )(-4y 4 )= 3 y 2 -4 y 4 = (3 -4)(y 2 y 4 )= -12y 6 = 3 2+4 = x 9 = z 10

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Zero exponent a 0 = 1, a 0 Note: 0 0 is undefined. Simplify each of the following expressions. 5 0 Example = 1 (xyz 3 ) 0 = x 0 y 0 (z 3 ) 0 = 1 1 1 = 1 -x0-x0 = -1∙x 0 = -1 ∙1 = -1 (Assume all variables have nonzero values.)

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Problem from today’s homework:

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Quotient Rule (applies to common bases only) Example Simplify the following expression. Group common bases together

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Problem from today’s homework:

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Power Rule: (a m ) n = a mn Note that you MULTIPLY the exponents in this case. Example Simplify each of the following expressions. (2 3 ) 3 = 2 9 = 512 (x4)2(x4)2 = x 8 = 2 33 = x 42

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Compare the result of (2 3 ) 3 to the result of 2 3 ·2 3: 2 3 ·2 3 = 2 3+3 = 2 6 = 64 Compare the result of (x 4 ) 2 to the result of x 4 x 2 : x 4 ·x 2 = x 4+2 = x 6 CAUTION: Notice the importance of considering the effect of the parentheses in the preceding example. (2 3 ) 3 = 2 9 = 512= 2 33 (x4)2(x4)2 = x 8 = x 42

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Power of a Product Rule (ab) n = a n b n Simplify (5x 2 y) 3 Example = 5 3 (x 2 ) 3 y 3 = 125x 6 y 3

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Example from today’s homework: (do this in your notebook) Answer: 36 a 18

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Power of a Quotient Rule Example Simplify the following expression. (Power of product rule in this step) (Power rule in this step)

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(All of these are on your formula sheet – use it while you do the homework.) Summary of exponent rules If m and n are integers and a and b are real numbers, then: Product Rule for exponents a m a n = a m+n Power Rule for exponents (a m ) n = a mn Power of a Product (ab) n = a n b n Power of a Quotient Quotient Rule for exponents Zero exponent a 0 = 1, a 0

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The assignment on today’s material (HW 5.1) is due at the start of the next class session. Lab hours in 203: Monday – Thursday, 8:00 a.m. to 7:30 p.m. Please remember to sign in!

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