# Mod 15 Study Guide

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MOD 15 - STUDY GUIDE
You may use a four function calculator.
Work with radicals and integer exponents
I can create equivalent numerical expressions using the properties of integer exponents.
1) Simplify the expression 45 ∙ 42
a) Using exponents:
b) Evaluate:
35
33
a) Using exponents:
b) Evaluate:
3) Find the value of x to make the statement
true.
(𝑏 4 )𝑥 = 𝑏16
\
2) Simplify the expression
4) What is the value of 5−3 ?
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5) Choose all the expressions that are
equivalent to
55
6) Use properties of exponents to find the
value of x.
55
Hint: you want to make the left side equal to the
right side.
44 ∙ 43 ∙ 4𝑥 =
410
42
7) Simplify the expression.
(10 − 2)3 − 42 + (12 )3
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8.EE.3 Learning Target: Express quantities using integer powers of 10. Using scientific notation, describe the
relationship between quantities.
8.EE.4 Learning Target: Perform operations using scientific notation. Describe and interpret real-world situations using
scientific notation.
8) Write in standard form.
1.09 &times; 106
6.21 &times; 100
8.52 &times; 10−3
7 &times; 10−5
9) Write in scientific notation.
93,000,000
1,637,000,000
0.000435
0.00103
27 &times; 102
25.7 &times; 104
13 &times; 10−2
4.5 &times; 10−3
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Write the numbers from smallest to largest.
3 &times; 103 ,
4 &times; 102 ,
3.2 &times; 10−3 ,
4 &times; 10−3
2 &times; 105 ,
3 &times; 104 ,
2.3 &times; 10−5 ,
1 &times; 105
11)
Estimate the state populations as a single-digit integers times a power of 10.
State
2012 population
Estimated 2012 population
California
38,041,430
4 &times; 107
Texas
26,059,203
New York
19,570,261
Florida
19,317,568
Illinois
12,875,255
12)
Circle all of the measurements that would most likely be recorded in scientific notation.
Distance between planets
Mass of an electron in grams
Distance from Chicago to New York in miles
Weight of a suitcase in pounds
Number of stars in the universe
Ounces of milk in a glass
Number of people in the world
Gallons of water in Lake Michigan
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Choose the most appropriate unit of measurement to use.
seconds
years
distance from California to New York
inches
feet
weight of an atom
milligrams
grams
miles
kilograms
Evaluate the expression. Write in scientific notation.
(𝟗 &times; 𝟏𝟎𝟔 ) + (𝟕 &times; 𝟏𝟎𝟔 )
(𝟗 &times; 𝟏𝟎𝟔 ) − (𝟕 &times; 𝟏𝟎𝟔 )
(𝟏. 𝟐 &times; 𝟏𝟎𝟓 ) + (𝟑. 𝟕 &times; 𝟏𝟎𝟑 )
(𝟗. 𝟖 &times; 𝟏𝟎𝟒 ) − (𝟏 &times; 𝟏𝟎𝟑 )
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Evaluate the expression. Write in scientific notation.
(𝟔 &times; 𝟏𝟎−𝟐 )(𝟑 &times; 𝟏𝟎𝟒 )
(𝟐. 𝟏 &times; 𝟏𝟎𝟔 )(𝟑 &times; 𝟏𝟎−𝟏𝟎 )
(𝟗 &times; 𝟏𝟎𝟖 )
(𝟐 &times; 𝟏𝟎𝟒 )
(𝟑. 𝟔 &times; 𝟏𝟎𝟒 )
(𝟔 &times; 𝟏𝟎−𝟓 )
(𝟐 &times; 𝟏𝟎𝟏𝟓 )
(𝟖 &times; 𝟏𝟎𝟕 )
(𝟗 &times; 𝟏𝟎−𝟑 )
(𝟑 &times; 𝟏𝟎−𝟕 )
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