Exponents and Scientific Notation Summative Review

Expanded Form, Exponential Form, and Negative Exponents

100

Write 4x4x4x4x4x4x4 in exponential form

4⁷

200

Write 3⁵ in expanded form.

3x3x3x3x3

300

Simplify the expression: x^-3

1/x³

400

Evaluate the expression: (149)⁰

1

500

Simplify the expression: 9b⁵x^-6

9b⁵/x⁶

Properties of Exponents

100

Evaluate the expression: (2²)³

2⁶

200

Simplify the expression: (4³y)³

4⁹y³

300

Simplify the expression: x⁵*x⁹

x¹⁴

400

Simplify the expression: (36x⁴y³)÷(6xy²)

6x³y

500

Simplify the expression: 5x÷7⁰

5x

Scientific Notation and Standard Form

100

Is the following expression written in scientific notation? If not, explain why. 32.5 * 10⁵

No, 32.5 is not between 1 and 10

200

Write 300 in scientific notation.

3 x 10²

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 how you know.

The Sahara desert is bigger because the exponent is bigger.

500

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

1.9 x 10²⁷

Multiplying and Dividing Scientific Notation

100

Solve the expression. Write your answer in scientific notation. (2 x 10⁹) * (4 x 10⁹)

8 x 10¹⁸

200

Solve the expression. Write your answer in scientific notation and round to 2 decimal places. (8.45 x 10¹⁰) ÷ (6.9 x 10⁵)

1.22 x 10⁵

300

Solve the expression. Write your answer in scientific notation. (54.1 x 10¹²) ÷  (3.61 x 10⁸)

1.499 x 10⁵

400

Solve the expression. Write your answer in scientific notation. (8 x 10⁴) x (2.1875 x 10^-3)

1.75 x 10²

500

An airplane traveled at a speed of 5.7 x 10² miles per hour for 1.4 x 10¹ hours. How far did the plane travel?

7.98 x 10³

Miscellaneous

100

Which number is smaller, 0.004 or (4 x 10^-2)?

0.004

200

Shelly's work is shown below: (5⁴)(5^-3) = 5. Is Shelly correct? Explain.

4 + (-3) = 1 and the base is 5. Since 5¹ = 5, Shelly is correct.

300

Is the following number written in scientific notation? Why or why not? 13.79 x 10⁷

No, 13.79 is greater than 10.

400

The mass of Mars is about 6.4 x 10²³ kg. It would take about 2.97 x 10³ times of the planet Mars to equal the mass of Jupiter. What is the mass of Jupiter?

1.9008 x 10²⁷

500

Brandon solved the problem shown below: (2 x 10⁴)(1.8 x 10⁶) = 3.6 x 10^-2 Is he correct? Explain.

No. He was supposed to add the exponents, not subtract.