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- Core Connections Integrated I, 2013
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6.2E: Exercises
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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?
COMMENTS
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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! 6-46. Louis is dilating triangle ABC at right. He multiplied
6-54. Consider the Equation Mat at right. Hint: Write the original equation represented. Simplify the tiles on the mat as much as possible. What value of x will make the two expressions equal? Bringing more math to more students.
Click on the link below for the "6-1, 6-2, and 6-3 Student eTools (CPM)"
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
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. Show more. Core Connections Integrated I, 2013. ISBN: 9781603283083. undefined Textbooks Show chapters.
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.
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Our resource for Core Connections Algebra 2 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 ...
Homework 1. 2 groups of 5 clouds circled; 2 rows of 5 clouds drawn 2. 3 groups of 4 diamonds circled; 3 rows and 3 columns of 4 diamonds each drawn. 3. 4 groups of 4 circles circled; 4 rows and columns of 4 circles each drawn. 4. a. 5 rows and 3 columns circled. b. 4 rows and 3 columns circled. 5.
Our expert help has broken down your problem into an easy-to-learn solution you can count on. See Answer See Answer See Answer done loading Question: Exercise 6.2.2: Repeat Exercise 6.2.1 for the following assignment statements: i. a=b[1]+c[d].
Find an exponential function that passes through the points ( − 2, 6) and (2, 1). Solution. Because we don't have the initial value, we substitute both points into an equation of the form f(x) = abx, and then solve the system for a and b. Substituting ( − 2, 6) gives 6 = ab − 2. Substituting (2, 1) gives 1 = ab2.
Answer to Solved 6.2.5 Exercises for Section 6.2 Exercise 6.2.1: | Chegg.com
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View Homework Help - Ch 5 Answers (to post) (8).pdf from MATH 1-2 at Westview High Scho... homework. Chapter 6 Textbook Solutions.pdf. No School. AA 1. Trigonometry. triangle. CPM Educational Program. Chapter 6 Textbook Solutions.pdf. θ cos 1 26 4 5 2 2 4 2 6 2 52 156371º c θ cos 1 2 35 3 562 3 2 5 2 5 3 2 6 2 from AA 1.
From Open Up Resources, https://openupresources.org/ Grade 6 Unit 2 Lesson 1
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.
c. The doorway height that would allow 40% of men to fit without bending is 66.2 in. The lengths of pregnancies are normally distributed with a mean of 267 days and a standard deviation of 15 days. a. Find the probability of a pregnancy lasting 308 days or longer. b.