- Get started
- Pre-Algebra
A quicker path to better grades
We have gathered all your curriculum-based courses, assignments, hints, tests, and solutions in one easy-to-use place
- Integrated I
- Integrated II
- Integrated III
Can't find your textbook?
More math. less studying.
A personal private tutor for each student. Free from preassure and study anxiety.
CPM Educational Program
- Core Connections Integrated I, 2013
- Core Connections Algebra 1, 2013
- Core Connections Geometry, 2013
- Core Connections Algebra 2, 2013
- Core Connections Integrated I, 2014
- Core Connections Integrated II, 2015
- Core Connections: Course 1
- Core Connections: Course 2
- Core Connections: Course 3
- Core Connections Integrated III, 2015
Expert Textbook Solutions
Browse your textbook to find expert solutions, hints, and answers for all exercises. The solutions are always presented as a clear and concise, step-by-step explanation with included theory and helpful figures, graphs, and diagrams. Mathleaks covers the most commonly adopted textbooks with more than 250000 expert solutions.
Mathleaks Solver
With Mathleaks, you’re not tied to your textbook for solutions. Instead, scan and solve exercises with our math solver, which instantly reads the problem by using the camera on your smartphone or tablet. Access the solver through the Mathleaks app or on our website. The Mathleaks solver works for Pre-Algebra, Algebra 1, and Algebra 2.
Mathleaks Community
Get access to the world's most popular math community with Mathleaks. You can connect with other students all over the US who are studying with the same textbook or in the same math course.
Study math more efficiently using Mathleaks for CPM Educational Program textbooks.
- school Campus Bookshelves
- menu_book Bookshelves
- perm_media Learning Objects
- login Login
- how_to_reg Request Instructor Account
- hub Instructor Commons
- Download Page (PDF)
- Download Full Book (PDF)
- Periodic Table
- Physics Constants
- Scientific Calculator
- Reference & Cite
- Tools expand_more
- Readability
selected template will load here
This action is not available.
6.2E: Exercises
- Last updated
- Save as PDF
- Page ID 30536
Practice Makes Perfect
Simplify Expressions with Exponents
In the following exercises, simplify each expression with exponents.
- \((\frac{1}{3})^2\)
- \((0.2)^4\)
- \((\frac{2}{9})^2\)
- \((0.5)^3\)
- \(\frac{4}{81}\)
- \((\frac{2}{5})^3\)
- \((0.7)^2\)
- \((\frac{3}{4})^3\)
- \((0.4)^3\)
- \(\frac{27}{64}\)
- \((−6)^4\)
- \(−6^4\)
- \((−2)^6\)
- \(−2^6\)
- \(−(\frac{1}{4})^4\)
- \((−\frac{1}{4})^4\)
- \(−(\frac{2}{3})^2\)
- \((−\frac{2}{3})^2\)
- \(−\frac{4}{9}\)
- \(\frac{4}{9}\)
- \(−0.5^2\)
- \((−0.5)^2\)
Exercise 10
- \(−0.1^4\)
- \((−0.1)^4\)
- −0.0001
Simplify Expressions Using the Product Property for Exponents
In the following exercises, simplify each expression using the Product Property for Exponents.
Exercise 11
\(d^3·d^6\)
Exercise 12
\(x^4·x^2\)
Exercise 13
\(n^{19}·n^{12}\)
Exercise 14
\(q^{27}·q^{15}\)
Exercise 15
- \(4^5·4^9\)
- \(8^9·8\)
Exercise 16
- \(3^{10}·3^6\)
- \(5·5^{4}\)
Exercise 17
- \(y·y^3\)
- \(z^{25}·z^8\)
Exercise 18
- \(w^5·w\)
- \(u^{41}·u^{53}\)
Exercise 19
\(w·w^2·w^3\)
Exercise 20
\(y·y^3·y^5\)
Exercise 21
\(a^4·a^3·a^9\)
Exercise 22
\(c^5·c^{11}·c^2\)
Exercise 23
\(m^x·m^3\)
Exercise 24
\(n^y·n^2\)
\(n^{y+2}\)
Exercise 25
\(y^a·y^b\)
Exercise 26
\(x^p·x^q\)
\(x^{p+q}\)
In the following exercises, simplify each expression using the Power Property for Exponents.
Exercise 27
- \((m^4)^2\)
- \( (10^3)^6\)
Exercise 28
- \((b^2)^7\)
- \((3^8)^2\)
Exercise 29
- \((y^3)^x\)
- \((5^x)^y\)
Exercise 30
- \((x^2)^y\)
- \((7^a)^b\)
Simplify Expressions Using the Product to a Power Property
In the following exercises, simplify each expression using the Product to a Power Property.
Exercise 31
- \((3xy)^2\)
Exercise 32
- \((4ab)^2\)
- \(16a^{2}b^{2}\)
Exercise 33
- \((−4m)^3\)
- \((5ab)^3\)
Exercise 34
- \((−7n)^3\)
- \((3xyz)^4\)
- \(−343n^3\)
- \(81x^{4}y^{4}z^{4}\)
Simplify Expressions by Applying Several Properties
In the following exercises, simplify each expression.
Exercise 35
- \((y^2)^4·(y^3)^2\)
- \((10a^{2}b)^3\)
Exercise 36
- \((w^4)^3·(w^5)^2\)
- \((2xy^4)^5\)
- \(32x^{5}y^{20}\)
Exercise 37
- \((−2r^{3}s^2)^4\)
- \((m^5)^3·(m^9)^4\)
Exercise 38
- \((−10q^{2}p^4)^3\)
- \((n^3)^{10}·(n^5)^2\)
- \(−1000q^{6}p^{12}\)
Exercise 39
- \((3x)^{2}(5x)\)
- \((5t^2)^{3}(3t)^{2}\)
Exercise 40
- \((2y)^{3}(6y)\)
- \((10k^4)^{3}(5k^6)^{2}\)
- \(25,000k^{24}\)
Exercise 41
- \((5a)^{2}(2a)^3\)
- \((12y^2)^{3}(23y)^2\)
Exercise 42
- \((4b)^{2}(3b)^{3}\)
- \((12j^2)^{5}(25j^3)^2\)
- \(1200j^{16}\)
Exercise 43
- \((25x^{2}y)^3\)
- \((89xy^4)^2\)
Exercise 44
- \((2r^2)^{3}(4r)^2\)
- \((3x^3)^{3}(x^5)^4\)
- \(128r^{8}\)
- \(27x^{29}\)
Exercise 45
- \((m^{2}n)^{2}(2mn^5)^4\)
- \((3pq^4)^{2}(6p^{6}q)^2\)
In the following exercises, multiply the monomials.
Exercise 46
\((6y^7)(−3y^4)\)
\(−18y^{11}\)
Exercise 47
\((−10x^5)(−3x^3)\)
Exercise 48
\((−8u^6)(−9u)\)
\(72u^{7}\)
Exercise 49
\((−6c^4)(−12c)\)
Exercise 50
\((\frac{1}{5}f^8)(20f^3)\)
\(4f^{11}\)
Exercise 51
\((\frac{1}{4}d^5)(36d^2)\)
Exercise 52
\((4a^{3}b)(9a^{2}b^6)\)
\(36a^{5}b^7\)
Exercise 53
\((6m^{4}n^3)(7mn^5)\)
Exercise 54
\((\dfrac{4}{7}rs^2)(14rs^3)\)
\(8r^{2}s^5\)
Exercise 55
\((\dfrac{5}{8}x^{3}y)(24x^{5}y)\)
Exercise 56
\((\frac{2}{3}x^{2}y)(\frac{3}{4}xy^2)\)
\(\frac{1}{2}x^{3}y^3\)
Exercise 57
\((\dfrac{3}{5}m^{3}n^2)(\dfrac{5}{9}m^{2}n^3)\)
Mixed Practice
Exercise 58
\((x^2)^4·(x^3)^2\)
Exercise 59
\((y^4)^3·(y^5)^2\)
Exercise 60
\((a^2)^6·(a^3)^8\)
Exercise 61
\((b^7)^5·(b^2)^6\)
Exercise 62
\((2m^6)^3\)
\(8m^{18}\)
Exercise 63
\((3y^2)^4\)
Exercise 64
\((10x^{2}y)^3\)
\(1000x^{6}y^3\)
Exercise 65
\((2mn^4)^5\)
Exercise 66
\((−2a^{3}b^2)^4\)
\(16a^{12}b^8\)
Exercise 67
\((−10u^{2}v^4)^3\)
Exercise 68
\((\frac{2}{3}x^{2}y)^3\)
\(\frac{8}{27}x^{6}y^3\)
Exercise 69
\((\frac{7}{9}pq^4)^2\)
Exercise 70
\((8a^3)^{2}(2a)^4\)
\(1024a^{10}\)
Exercise 71
\((5r^2)^{3}(3r)^2\)
Exercise 72
\((10p^4)^{3}(5p^6)^2\)
\(25000p^{24}\)
Exercise 73
\((4x^3)^{3}(2x^5)^4\)
Exercise 74
\((\frac{1}{2}x^{2}y^3)^{4}(4x^{5}y^3)^2\)
\(x^{18}y^{18}\)
Exercise 75
\((\frac{1}{3}m^{3}n^2)^{4}(9m^{8}n^3)^2\)
Exercise 76
\((3m^{2}n)^{2}(2mn^5)^4\)
\(144m^{8}n^{22}\)
Exercise 77
\((2pq^4)^{3}(5p^{6}q)^2\)
Everyday Math
Exercise 78
Email Kate emails a flyer to ten of her friends and tells them to forward it to ten of their friends, who forward it to ten of their friends, and so on. The number of people who receive the email on the second round is \(10^2\), on the third round is \(10^3\), as shown in the table below. How many people will receive the email on the sixth round? Simplify the expression to show the number of people who receive the email.
Exercise 79
Salary Jamal’s boss gives him a 3% raise every year on his birthday. This means that each year, Jamal’s salary is 1.03 times his last year’s salary. If his original salary was $35,000, his salary after 1 year was $35,000(1.03), after 2 years was $\(35,000(1.03)^2\), after 3 years was $\(35,000(1.03)^3\), as shown in the table below. What will Jamal’s salary be after 10 years? Simplify the expression, to show Jamal’s salary in dollars.
Exercise 80
Clearance A department store is clearing out merchandise in order to make room for new inventory. The plan is to mark down items by 30% each week. This means that each week the cost of an item is 70% of the previous week’s cost. If the original cost of a sofa was $1,000, the cost for the first week would be $1,000(0.70) and the cost of the item during the second week would be $\(1,000(0.70)^2\). Complete the table shown below. What will be the cost of the sofa during the fifth week? Simplify the expression, to show the cost in dollars.
Exercise 81
Depreciation Once a new car is driven away from the dealer, it begins to lose value. Each year, a car loses 10% of its value. This means that each year the value of a car is 90% of the previous year’s value. If a new car was purchased for $20,000, the value at the end of the first year would be $20,000(0.90) and the value of the car after the end of the second year would be $\(20,000(0.90)^2\). Complete the table shown below. What will be the value of the car at the end of the eighth year? Simplify the expression, to show the value in dollars.
Writing Exercises
Exercise 82
Use the Product Property for Exponents to explain why \(x·x=x^2\)
Answers will vary.
Exercise 83
Explain why \(−5^3=(−5)^3\), but \(−5^4 \ne (−5)^4\).
Exercise 84
Jorge thinks \((\frac{1}{2})^2\) is 1. What is wrong with his reasoning?
Exercise 85
Explain why \(x^3·x^5\) is \(x^8\), and not \(x^{15}\).
a. After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
b. After reviewing this checklist, what will you do to become confident for all goals?
Home > INT3
© 2022 CPM Educational Program. All rights reserved.
IMAGES
VIDEO
COMMENTS
CPM Education Program proudly works to offer more and better math education to more students.
CPM Education Program proudly works to offer more and better math education to more students.
Microsoft Word - HW 6.2.2 Parametric Functions.docx. Selected Answers: 1. 3. 5. 13. From the first equation, = 5 − . Substituting into the second equation, 8 − 10 + 2 , so the Cartesian equation is = 2 − 2.
Homework Name _____ Period _____ Work through each of the problems below to practice the concepts from today's lesson and review concepts from previous lessons. Be sure to always show all work! 6-58. Graph the triangle at right. Multiply the y-coordinate of each point by 4. Then graph the new shape.
Mathleaks offers homework help with answers, hints, and learning-focused solutions for textbooks in Integrated Mathematics II, 9th and 10th grade. The solutions include theory and alternative ways of solving the problems, and cover textbooks from publishers such as Houghton Mifflin Harcourt, McGraw Hill, CPM, Big Ideas Learning, and Pearson. ...
Exercise 46. Exercise 47. Exercise 48. Exercise 49. Exercise 50. Find step-by-step solutions and answers to CPM Geometry - 9781885145703, as well as thousands of textbooks so you can move forward with confidence.
High School Series. 3 years of a 5-year sequence of college. preparatory mathematics courses in. English and Spanish. Core Connections Algebra. Core Connections Geometry. Core Connections Algebra 2.
Mathleaks offers the ultimate homework help and much of the content is free to use. Browse the textbooks below or by downloading the Mathleaks app for free on Google Play or the App Store. Start CPM Educational Program. CPM Educational Program. Show more. Core Connections Integrated I, 2013. ISBN: 9781603283083.
6-58. Create a large coordinate graph on graph paper and graph the triangle at right. Multiply the y - coordinate of each point by 4. Then graph the new shape. Make sure you connect your points. List the points for the new shape.
Our resource for Core Connections Course 3 includes answers to chapter exercises, as well as detailed information to walk you through the process step by step. With Expert Solutions for thousands of practice problems, you can take the guesswork out of studying and move forward with confidence. Find step-by-step solutions and answers to Core ...
Algebra, Geometry, & Algebra 2 Table of Contents Core Connections Algebra Chapter 1: Functions Section 1.1 1.1.1 Solving Puzzles in Teams 1.1.2 Investigating the Growth of Patterns 1.1.3 Investigating the Graphs of Quadratic Functions Section 1.2 1.2.1 Describing a Graph 1.2.2 Cube Root and Absolute Value Functions 1.2.3 Function Machines 1.2.4 Functions 1.2.5 Domain and
Exercise 9. Exercise 10. Exercise 11. Exercise 12. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Core Connections Geometry 2nd Edition, you'll learn how to solve your toughest homework problems.
Use the eTools below to compare the given Expression Mats in each problem and determine which is greater.
Answer to Solved 6.2.5 Exercises for Section 6.2 Exercise 6.2.1: | Chegg.com
These videos were created to support both students and teachers with the OUR (Open Up Resources) Mathematics curriculum. Initially, the full lessons were created as a resource for teachers when ...
Exercise 5. At Quizlet, we're giving you the tools you need to take on any subject without having to carry around solutions manuals or printing out PDFs! Now, with expert-verified solutions from Microeconomics 6th Edition, you'll learn how to solve your toughest homework problems. Our resource for Microeconomics includes answers to chapter ...
Exercise 79. Salary Jamal's boss gives him a 3% raise every year on his birthday. This means that each year, Jamal's salary is 1.03 times his last year's salary. If his original salary was $35,000, his salary after 1 year was $35,000 (1.03), after 2 years was $ 35, 000(1.03)2, after 3 years was $ 35, 000(1.03)3, as shown in the table below.
CPM Education Program proudly works to offer more and better math education to more students.
Engineering. Computer Science. Computer Science questions and answers. Exercise 6.2.2: Repeat Exercise 6.2.1 for the following assignment state- ments: i. a b [i] + c [j]. ii. a [i] = b*c b*d. iii. x = f (y+1) + 2. iv. x = *p + &y. Question: Exercise 6.2.2: Repeat Exercise 6.2.1 for the following assignment state- ments: i. a b [i] + c [j].
CPM Education Program proudly works to offer more and better math education to more students.
CPM Education Program proudly works to offer more and better math education to more students.