 # 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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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.)

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

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

Section 5.1 Exponents

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.

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

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.)

Problem from today’s homework:

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

Problem from today’s homework:

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

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

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

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

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

(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

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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