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IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
CPM Materials modified by Mr. Deyo
What part of the expression is being raised to a power?
What are the factors?
How can we rewrite the expression to have fewer
terms?
Common Core Standard: 8.EE.1
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
By the end of the period, I will develop methods for simplifying expressions with positive exponents, and will explain the difference between raising a single number to a power and raising a grouped quantity to a power.
I will demonstrate this by completing Four‑Square notes and by solving problems in a pair/group activity.
Learning TargetTitle: IM8 ‑ Ch. 8.2.2 How Can I Write It In Simpler Form? Date:
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
Home Work: Sec. 8.2.2Desc. Date Due
Review & Preview
3 Problems 8‑66, 8‑68, 8‑69
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
Vocabulary1) Base
2) Exponent
3) Factored Form
4) Simplified Exponent Form
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
8.2.2 How Can I Write It In Simpler Form?In the previous lesson, you expanded expressions written with exponents into factored form and then rewrote them in simpler form. You also looked at ways to rewrite very large numbers in scientific notation to compare them more easily. In this lesson, you will continue to develop ways to rewrite expressions using exponents. Use the questions below to focus discussion in your study team.
What part of the expression is being raised to a power?
What are the factors?
How can we rewrite the expression to have fewer
terms?
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
859. Rewrite each expression below in a simpler form.
a) 102 · x3 · 10 · y
b) 203 · 208
c) x2y2z2 · x3z5
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
860. Erin wants to rewrite the expression 52x2 · 54x3 in simpler form. She started by expanding the expression like this:
5 · 5 + x · x + 5 · 5 · 5 · 5 + x · x · x
25 + x2 + 625 + x3
Do you agree with her work so far? Work with your team to complete the problem or, if you do not agree, to write Erin a note explaining how to correct her work and find the correct simplification.
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
861a. When a number is raised to a power, and then raised to a power again, the result follows a consistent pattern. Complete the table. Expand each expression into factored form and then rewrite it with new exponents as shown in the example.
a) Work with your team to describe the pattern between the exponents in the original form and the exponent(s) in the simplified exponent form.
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
861b. When a number is raised to a power, and then raised to a power again, the result follows a consistent pattern.
b) Visualize (203)8 written in factored form. What is multiplied? That is, what is the base? How many times is it multiplied? Use the expression you visualized to help you rewrite the expression in simplified exponent form. Describe in detail how you figured out what exponent to use in the simplified exponent form.
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
862. In problem 859 you simplified the expression 203 · 208. Compare the factored form you wrote for that expression to the expression you visualized in part (b) of problem 861. How are the two expressions different?
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
863. Heidi is trying to rewrite the two expressions: (2x)3 2x3"Are these two ways of writing the same thing?
Or do they mean something different? " Heidi wonders.
a) Rewrite (2x)3 by expanding and then simplifying.What part is being raised to the third power?
b) Heidi thinks 2x3 is the same as 2 · x3. Show that she is correct by expanding the expression.
c) Are (2x)3 and 2x3 equivalent? Explain why or why not.
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
864. AJ was trying to simplify the exponent expression: He started by writing out the factored form. Once he saw the factors he recognized a Giant One in his work.
5753
a) Write out the factored form. Where did he see a Giant One?
b) Work with your study team to use the Giant One to simplify and rewrite AJ’s expression. What is the result?
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
a)
c)
865. Expand each expression below into factored form. Then rewrite it in simplified exponent form.
2 b)
d)
4
2234
35
y7
y4x y3 2
x y2
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
a)
c)
866. Simplify each expression.
3 5 8 b)
d)
2 3 (3x)4
33 13
27 94 2
9 73 2
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.2/problem/866
3 5 8 3. ...
.35.( ) ..
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
867. Janet lit a 12‑inch candle. She noticed that it was getting an inch shorter every 30 minutes.
a) Is the association between the time the candle is lit and the height of the candle positive or negative?
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.2/problem/867
b) In how many hours will the candle burn out? Support your answer with a reason.
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
868. Show the “check” for each of the problems below. Write whether the solution is correct or incorrect.
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.2/problem/868
a) For 3x + 2 = x − 2,
does x = 0?
b) For 3(x − 2) = 30 + x − 2 − x + 2,
does x = 12?
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
869. On graph paper, graph the shape that has coordinates A(−2, −1), B(1, 2), and C(−2, 3).a) Predict the coordinates of the shape after it is translated three units to the right and one unit down. Check your prediction on the graph.
https://www.desmos.com/calculator/p9vuqyzrnv http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.2/problem/869
A'( , ) B'( , )C'( , )
b) Dilate the original shape by multiplying both the x‑ and y‑coordinates by 2. What are the new coordinates?
c) Reflect the original shape over the y‑axis. What are the new coordinates?
A"'( , ) B"'( , )C"'( , )
A''( , ) B''( , )C''( , )
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
870. Solve the equations below for the indicated variable.
a) 3(2x − 1) + 2y = 5x for y b) 600x + 200y = 500x for x
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.2/problem/870
IM 8 Ch 8.2.2 How Can I Write It In Simpler Form
a)
c)
871. Use <, >, or = to compare the number pairs below.
0.183 ___ 0.18
b)
d)
http://homework.cpm.org/cpmhomework/homework/category/CC/textbook/CC3/chapter/Ch8/lesson/8.2.2/problem/871
f)
e)
−13 ___ −17
0.125 ____18
−6 ___ −4
72%____ 3530
−0.25 ____ −0.05