Unit 8 Review

Exponents

100

Write 4x4x4x4x4x4x4 in exponential form. 

4⁷

200

Write 3⁵ in expanded form.

3x3x3x3x3

300

Evaluate the expression: -3³

-27

400

Evaluate the expression: 149⁰

1

500

Evaluate the expression: 9^-2

1/81

Laws of Exponents

100

Evaluate: (2²)³

4³ = 64 or 2⁶ = 64

200

Simplify: (4y)³

64y³

300

Simplify: (x⁵)(x⁹)

x¹⁴

400

Simplify: (36x⁴y³)/(6xy²)

6x³y

500

Simplify: (5x²)³/(7y⁹)⁰

125x⁶

Scientific Notation

100

Is the following expression written in scientific notation? If not, explain why. 

3.25 + 10^-7

No, it should be multiplied, not added.

200

The mass of Jupiter is approximately 1,900,000,000,000,000 kg. Write the mass of Jupiter in scientific notation.

1.9 x 10¹⁵

300

The mass of a Monarch butterfly is about 9.5 x 10^-3. Write this number in standard form.

.0095

400

The size of the Sahara desert is about 3.629 x 10⁶ square miles and the Arabian desert is about 9 x 10⁵ square miles. Which desert is larger? Explain your reasoning.

The Sahara desert because the exponent is bigger.

500

The size of the four oceans, in square km, is shown below. List the oceans from smallest to largest.

Pacific Ocean: 1.7965 x 10⁸ 

Arctic Ocean: 1.323 x 10⁷ 

Atlantic Ocean: 1.061 x 10⁸

Indian Ocean: 7.49 x 10⁷

Arctic, Indian, Atlantic, and Pacific. 

Operations with Scientific Notation

100

Solve the expression. Write your answer in scientific notation. (3.7 x 10⁹) + (9.04 x 10⁹)

12.74 x 10⁹ = 1.274 x 10¹⁰

200

Solve the expression. Write your answer in scientific notation. (8.45 x 10^-7) - (6.9 x 10^-7)

1.55 x 10^-7

300

The surface of the Earth is water and land. The approximate total surface area of Earth is 5.1 x 10⁸ km2 and the approximate total surface area of water is 361,000,000 km2. About how much of Earth's surface area is land?

1.49 x 10⁸

400

Humpback whales are known to weigh as much as 8 x 10⁴ pounds. The krill they eat weighs only 2.1875 x 10^-3 pounds. Approximately how many times greater than the krill are humpback whales?

4 x 10⁷

500

A computer can perform 4.66 x 10⁸ instructions per second. How many instructions is that per minute? Per hour? Write your answers in scientific notation.

Per Second = 2.796 x 10¹⁰

Per Hour = 1.6776 x 10¹²

Multiplying and Factoring Expressions

100

Use the distributive property to simplify: 5x(x+2)

5x²+10x

200

Factor the expression using the GCF: 4x²+6x

2x(2x+3)

300

Find the product: 3n(1/3n - 2/3)

n²-2n

400

Factor the expression using the GCF: 28a⁵b + 20a²b

4a²b(7a³+5)

500

Factor the expression using the GCF: 

-12x⁵y³-9x⁴y²-12x⁴y

3x⁴y(-4xy²-3y-4)