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Please open Daily Quiz 34. A scientific calculator may be used on this quiz. You can keep your yellow formula sheets out when you take the quiz. Remember to turn in your answer sheet to the TA when the quiz time is up. If you have any time left after finishing the quiz problems, CHECK YOUR ANSWERS before you submit the quiz.

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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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Last two weeks of class: Today: (Monday, 12/2) Daily Quiz 34 on HW 39 due today on Section 10.1 Hand back/review Quiz 9 Lecture on Section 7.1/2 (Rational exponents) Tuesday –Thursday this week: Daily Quizzes on HW due each day (DQ 35, 36, 37) Lectures on last 3 new sections (10.3&4, 11.2, 11.5) NEXT WEEK: Monday, 12/9: Practice Weekly Quiz 10 due at start of class 10-15 minutes of Q&A and review 25-point Weekly Quiz 10 on all sections since Test 3 Tuesday –Thursday next week: Review lectures on Units 1-3 (Tests 1-3) Review HW on each unit, worth double points (8 pts each)

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Math 110 Final Exam: Comprehensive – covers the whole semester Worth 200 points (20% of course grade) 45 questions Test period is one hour and 50 minutes Practice Final will be worth 10 points and also has 45 questions and unlimited tries. Your best score on the practice final will also earn up to 20 extra credit points on the final. (more details next week)

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Make sure you know the day and time of the final exam for this section of Math 110: Day: ______ Date:______ Time: ______ to _______ All Math 110 finals will be given in your regular classroom. (Next slide shows final exam schedules for all sections.)

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Grade Scale Weekly Quiz 9 Results: Average class score after partial credit: __________ Commonly missed questions: #_________________ If you got less than 75% on this quiz, make sure to go over your test with me or a TA sometime in the next few days. This material will be covered on the next weekly quiz, and it will also be covered again on the final exam.

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Section 10.2 Radicals and Rational Exponents

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If n is a positive integer greater than 1 and a is a real number, then Definition of a rational exponent in terms of a radical:

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Recall that a cube root is defined so that However, if we let b = a 1/3, then Since both values of b give us the same a, Why does this definition make sense?

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Use radical notation to write the following. Simplify if possible. Example

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We can expand our use of rational exponents to include fractions of the type m/n, where m and n are both integers, n is positive, and a is a positive number,

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Use radical notation to write the following. Simplify if possible. Example

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Problem from today’s homework: 64

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Now to complete our definitions, we want to include negative rational exponents. If a -m/n is a nonzero real number,

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Use radical notation to write the following. Simplify if possible. Example What if the previous problem was ? The answer would be “N” (not a real number) because you’d be trying to take an even root of a negative number.

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All the properties that we have previously derived for integer exponents hold for rational number exponents, as well. We can use these properties to simplify expressions with rational exponents.

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Use properties of exponents to simplify the following. Write results with only positive exponents. Example What would this answer look like in radical form?

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Problem from today’s homework: Final answer: -b Hint: The exponent will be 2/5 + 1/5 – (-2/5). Then simplify the fraction.

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Use rational exponents to write as a single radical. Example

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Problem from today’s homework: Final answer: Hints: Start by writing each radical as a rational (fraction) exponent, then add the fractions by finding a common denominator. For your final step, convert back into radical form.

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REMINDER: The assignment on today’s material (HW 40) is due at the start of the next class session. Please open your laptops and work on the homework assignment until the end of the class period. Lab hours in 203: Mondays through Thursdays 8:00 a.m. to 7:30 p.m. Please remember to sign in on the Math 110 clipboard by the front door of the lab

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