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.

Please

CLOSE

YOUR LAPTOPS,and turn off and put away your

cell phones,

and get out your note-taking materials.

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)

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)

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.)

Grade ScaleGrade A A- B+ B B- C+ C

C- F

Points ≥ 920 ≥ 890 ≥ 860 ≥ 830 ≥ 800 ≥ 750 ≥ 700

≥ 670 < 670

% Score ≥ 92 ≥ 89 ≥ 86 ≥ 83 ≥ 80 ≥ 75 ≥ 70

≥ 67 < 67

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.

Section 10.2Radicals and Rational Exponents

nn aa /1

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:

Recall that a cube root is defined so that

abba 33 ifonly

However, if we let b = a1/3, then aaaab 133/133/13 )(

Since both values of b give us the same a,

33/1 aa

Why does this definition make sense?

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

3381 4 44 4/181

5/11032x 25 1055 10 2232 xxx

Example

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,

mnn mnm aaa /

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

3/48 4

3 8

Example

4

3 32 42 16

Problem from today’s homework:

64

Now to complete our definitions, we want to include negative rational exponents.

If a-m/n is a nonzero real number,

nmnm

aa

// 1

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

3/264 3/264

1

4/516 4/516

1

Example

23 64

1

23 34

1

24

116

1

54 42

1

52

1

32

1

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.

4/5)16(

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.

Use properties of exponents to simplify the following. Write results with only positive exponents.

33/25/132 x 25/332 x

3/2

2/14/1

a

aa 3/22/14/1a

Example

23

5 52 x 232 x 28x

12/812/612/3a 12/11a 12/11

1

a

What would this answer look like in radical form? 𝟏𝟏𝟐√𝒂𝟏𝟏

Problem from today’s homework:

Final answer: -b

Hint: The exponent will be 2/5 + 1/5 – (-2/5). Then simplify the fraction.

Use rational exponents to write as a single radical.

Example

253 2/13/1 25 6/36/2 25 6/132 25 6 200

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.

20 19y

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