Exponents and Scientific Notation

Square Roots and Cube Roots

100

Write m⁷ in expanded form

m × m × m × m × m × m × m

200

Evaluate the expression:(-9)²

81

300

Evaluate the expression: (2/7)³

8/343

400

Evaluate the expression: x³ =343

x = 7

500

The volume of a cube is V = 729 in³. 

Write an equation that could be used to find x (the length of one side of the cube).

Solve for x.

x³ = 729

x = 9 inches

Properties of Exponents

100

Simplify: x¹²/x⁸

x⁴

200

Simplify: x³ • x⁵

x⁸

300

Simplify: (x⁵)⁸

x⁴⁰

400

Simplify: (x²y²)³ • (x²)⁰

x⁶y⁶

500

Simplify: (xy)⁷/(x²y³)²

x³y

Scientific Notation (+/-)

100

Convert 0.000098 to scientific notation

9.8 × 10^-5

200

Find the sum or difference: (6.2 × 10⁸) + (2.3 × 10⁸)

8.5 × 10⁸

300

Find the sum or difference: (7.2 × 10^-3) - (6.8 × 10^-4)

6.52 × 10^-3

400

Find the sum or difference: (6.4 × 10⁵) + 320,000

9.6 × 10⁵

500

Find the sum or difference: 0.00054 - (3.2 × 10^-4)

2.2 × 10^-4

Scientific Notation (×/÷)

100

Estimate 789,000,350 in scientific notation

8 × 10⁸

200

Find the product or quotient: (1.5 × 10^-5)(5 × 10^-3)

7.5 × 10^-8

300

Find the product or quotient: (9.45 × 10⁷)/(2.1 × 10²)

4.5 × 10⁵

400

Find the product or quotient and write it in scientific and standard notation: (8 × 10^-3)(0.0003)

2.4 × 10^-6

0.0000024

500

Find the product or quotient and write it in scientific and standard notation: 5,000,000/(2.5 × 10³)

2 × 10³

2,000

Word Problems/Miscellaneous

100

Evaluate the expression: 9^-2

How could you write this without a negative exponent?

1/81

1/9²

200

There are approximately 1.2 × 10⁸ households in the U.S. If the average household uses 400 gallons of water each day, what is the total number of gallons of water used by households in the U.S. each day?

Write in scientific and standard notation.

4.8 × 10¹⁰ gallons

48,000,000,000 gallons

300

The population of China is about 1.4 × 10⁹ people, while the population of South Korea is approximately 50,000,000 people. How many times greater is the population of China than the population of South Korea?

Write in scientific and standard notation.

2.8 × 10¹ times greater

28 times greater

400

Summerville has a population of 430,000 people, while Eagleton has a population of 5.7 × 10⁵ people. What is the difference in population between the two towns?

Write in scientific and standard notation. 

1.4 × 10⁵

140,000

500

A snail in Lauren's vegetable garden is traveling at a speed of 0.03 miles per hour. An airplane flying above Lauren's house is traveling at a speed of 575 miles per hour. ESTIMATE how many times faster the airplane is traveling than the snail?

 Write in scientific and standard notation

2 × 10⁴ or 20,000 times faster