Module 1 Exponents and Scientific Notation

Powers and Exponents

100

Write the expression using exponents.  

(-7) times (-7) times 5 times 5 times 5 times 5 

-7²  times 5⁴

200

Evaluate the expression: 

3⁴ -(-4)²

65

300

Evaluate the expression

6 +2⁶

70

400

A scientist estimates that after a certain amount of time. there would be 2⁵ times 3³ times 10⁵ bacteria in a Petri dish.  How many bacteria is this?  

86,400,000

500

Louis is comparing the populations of several nearby cities.  The population of Liberty Crossing can be written as 4⁹ people, and the population of Harrisburg can be written as 4⁷ people.  The population of Glenview is 4³ times the population of Harrisburg.  Write the names of the cities from the city with the least population to the city with the greatest population.  

1.Harrisburg

2.Liberty Crossing 

3. Glenview 

Multiply/Divide Monomials

100

Simplify 5⁴ times 5

5⁵ or 3,125

200

Simplify m⁵ times m²

m⁷

300

b^{12 divided by} b⁵

b⁷

400

Simplify 5⁵ times 6³ times 8¹⁰ divided by 5³ times 6 times 8⁹

5² times 6² or 7,200 

500

A publisher sells 10⁶ copies of a new science fiction book and 10³ copies of a new mystery book.  How many times as many science fiction books were sold than mystery books?  

10³ or 1,000

Power of Monomials

100

Simplify expression: (7w⁷)³

343w²¹

200

Simplify (8³)³

8⁹ or 134,217,728

300

Simplify (7a⁵b⁶)⁴

2,401 a²⁰ b²⁴

400

Which is greater: 1,000 or (6²)^3? Explain.  

(6²)³ is larger because 46,656 is greater than 1,000 when you multiply base and exponents.  

500

A square floor has a side length of 7x⁵y⁶ units.  A square tile has a side length of x²y units.  How many tiles will it take to cover the floor?  

49x⁶ y¹⁰

Zero and Negative Exponents

100

Simplify 46⁰

1

200

Simplify 8^-4

1/8⁴

300

1/d⁶

d^-6

400

Simplify x^-8/x^-12

x⁴

500

Without evaluating, order 5^-7, 5⁴, and 5⁰ from LEAST (smallest) to GREATEST (largest).  Explain your reasoning.  

Least to Greatest: 

1. 5^-7

2.5⁰ 

3. 5⁴

Scientific Notation

100

Find the sum of (8.41 times 10³) + (9.71 times 10⁴⁾ 

1.0551 times 10 ⁵

200

(1.28 times 10⁵) + (1.13 times 10³) 

1.2913 times 10⁵

300

(7.26 times 10⁶) - (1.3 times 10⁴) 

7.247 times 10 ⁶

400

The population of Florida was recently recorded as 20,612,439 people.  Write an estimation in scientific notation for the population.  

2 times 10⁷ people 

500

The table shows the approximate population and land area for several states.  Which state has the LEAST population density?  

State        Population        Land Area (mi²) 

Arizona      6.83 times 10⁶     113, 594

Colorado    5.46 times 10⁶    103,642

Kentucky    4.43 times 10⁶    39,486

Minnesota   5.45 times 10⁶    79,627 

Colorado