For more information, please see full course syllabus of Pre Algebra

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For more information, please see full course syllabus of Pre Algebra

For more information, please see full course syllabus of Pre Algebra

### Positive Exponents

- To evaluate a base raised to an exponent, multiply the base or factor the number of times indicated by the exponent.
- The order of operations:
- Parentheses
- Exponents
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
- An exponent applies only to its base, so ( −4 )
^{2}= 16 but −4^{2}= −16.

### Positive Exponents

Write 7 · 7 · 7 · 7 · 5 · 5 using exponents.

- There are four 7s and two 5s.

7

^{4}·5^{2}Write 5 · 5 · 5 · ( - 2) · ( - 2) · ( - 2) · ( - 2) using exponents.

- There are three 5s and four (-2)s.

5

^{3}·( − 2)^{4}Write m · m · p · p · p · ( - 4) · ( - 4) using exponents .

- There are two ms, three ps, and two ( - 4)s.

m

^{2}·p^{3}·( − 4)^{2}Compare ( − 5)

^{4}to - 5^{4}.- ( − 5)
^{4}= ( − 5) ·( − 5) ·( − 5) ·( − 5) = - 25 ·25 =
- 625
- − 5
^{4}= − 5 ·5 ·5 ·5 = - − 25 ·25 =

- 625

Evaluate (5 ·m)

^{2}− 7 for m = 2- (5 ·2)
^{2}− 7 = - 10
^{2}− 7 = - 100 − 7 =

93

Evaluate (3y − 5)

^{2}+ 2y for y = 6- (3(6) − 5)
^{2}+ 2(6) = - (18 − 5)
^{2}+ 12 = - (3)
^{2}+ 12 = - 9 + 12 =

21

Evaluate (2r − s)

^{2}+ 3s for r = 6 and s = 2.- (2(6) − 2)
^{2}+ 3(2) = - (12 − 2)
^{2}+ 3(2) = - 10
^{2}+ 6 = - 100 + 6 =

106

Evaluate (x − 3y)

^{3}+ (4 − z)^{2}for x = 4, y = 2, and z = 2.- (4 − 3(2))
^{3}+ (4 − 2)^{2}= - (4 − 6)
^{3}+ (4 − 2)^{2}= - (−2)
^{3}+ (2)^{2}= - ( − 2) ·( − 2) ·( − 2) + 2 ·2 =

- 32

The formula h = 160t − t

^{2}is used to estimate the number of feet a ball rises in t seconds after it is thrown. How high is a ball 3 seconds after it is thrown?- h = 160t − t
^{2}, t = 3 feet - h = 160(3) − 3
^{2}feet - h = 480 − 9 feet

h = 371 feet

A certain type of bacteria doubles in population every 6 hours. Given that there were 10 bacteria to begin with, how many bacteria will there be after one day, assuming all of them stay alive?

- One day has 24 hours.
- After 6 hours, the bacteria population will be 10 × 2 bacteria.
- After 12 hours, the bacteria population will be 10 ×2 ×2 = 10 ×2
^{2}bacteria. - After 18 hours, the bacteria population will be 10 ×2 ×2 ×2 = 10 ×2
^{3}bacteria. - After 24 hours, the bacteria population will be 10 ×2 ×2 ×2 ×2 = 10 ×2
^{4}bacteria. - 10 ×2
^{4}= - 10 ×16 =

160 bacteria

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

Answer

### Positive Exponents

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

- Intro
- What You'll Learn and Why
- Vocabulary
- Vocabulary
- Writing Expressions with Exponents
- Writing Expressions with Exponents
- Simplifying Power
- Simplifying Power
- Order of Operations
- Order of Operations
- Evaluating Expressions with Exponents
- Extra Example 1: Evaluate
- Extra Example 2: Evaluate
- Extra Example 3: Height of the Rocket
- Extra Example 4: Number of Cells

- Intro 0:00
- What You'll Learn and Why 0:05
- Topics Overview
- Vocabulary 0:26
- Factor
- Exponent
- Vocabulary 1:57
- Base
- Power
- Writing Expressions with Exponents 2:31
- Example 1: Writing Expressions with Exponents
- Example 2: Writing Expressions with Exponents
- Writing Expressions with Exponents 3:20
- Example 3: Writing Expressions with Exponents
- Example 4: Writing Expressions with Exponents
- Simplifying Power 4:06
- Example 5: Simplifying Power
- Example 6: Simplifying Power
- Simplifying Power 6:06
- Example 7: Simplifying Power
- Example 8: Simplifying Power
- Order of Operations 7:24
- PEMDAS
- Order of Operations 8:32
- Multiplying/Dividing and Adding/Subtracting
- Evaluating Expressions with Exponents 10:07
- Example 9: Evaluating Expressions with Exponents
- Example 10: Evaluating Expressions with Exponents
- Extra Example 1: Evaluate 12:33
- Extra Example 2: Evaluate 13:42
- Extra Example 3: Height of the Rocket 15:00
- Extra Example 4: Number of Cells 16:38

0 answers

Post by sherman boey on August 4, 2014

error with practice question

Q. Evaluate (x âˆ’ 3y)3 + (4 âˆ’ z)2 for x = 4, y = 2, and z = 2.

the answer was -32 after this step ( âˆ’ 2) Â·( âˆ’ 2) Â·( âˆ’ 2) + 2 Â·2 = -4

it should be -4 not -32 correct me if i am wrong

0 answers

Post by Jason Volker on December 27, 2013

In the Practice Questions section (not in Prof. Fung's actual lecture) there are a few wrong answers given (I've double-checked the answers on Wolfram Alpha).

Practice Question no.6 the answer should be 181, not 21 as stated.

Practice Question no.8 the answer should be -4, not -32 as stated.

Practice Question no.9 the answer should be 471 feet, not 371 as stated.

As a side note, I very much enjoy Prof. Fung's teaching and consider her course to be of excellent quality.

0 answers

Post by Eric Kilgore on July 15, 2013

I appreciate your classes greatly.

2 answers

Last reply by: E Marrs

Sat Mar 21, 2015 5:51 PM

Post by Eric Kilgore on July 15, 2013

Professor,

I understand if you think I am trying to troll your class but I promise I am not. The first question I had was in reference to the equation in the practical exercise "(3y-5)squared +2y =". Specifically steps two and three.

(18-5)squared+12 =. Then step three says (3)squared + 12 =. Not (13) squared.

Eric

1 answer

Last reply by: Professor Fung

Thu Jul 11, 2013 5:37 AM

Post by Eric Kilgore on July 9, 2013

Professor,

After my previous post I believe there are incorrect answers on the next few questions also. Could someone please verify all the answers on the practical exercise and let me know if it was I who is making these mistakes.

Thank you.

1 answer

Last reply by: Professor Fung

Thu Jul 11, 2013 5:26 AM

Post by Eric Kilgore on July 9, 2013

Professor,

The practice question (3y-5)^2+2y I am not sure but I think there may be an error. 18-5 should be 13 correct? I am trying to study for my college entry exams and I am not sure if I have made a mistake with this problem or it was just a typo. Thank you.

0 answers

Post by philip schuyler on December 23, 2012

THere are 4 3's so that would be an even number..... your answer would be a positive 81