Exponent Review

Basic Exponents

100

Write the expression using exponents:

2*2*2*2*2

2⁵

200

Write this expression using exponents.

8*3*3*3*3*8*8*8*3

3^5*8^4

300

a*a*a*a*a*a

a⁶

400

(-11/14)(-11/14)(-11/14)(-11/14)

(-11/14)^4

500

Interstate 70 stretches almost

2^3*5^2*11

miles across the United States. About how many miles long is Interstate 70? Write your claim in a complete sentence, restating the question.

Interstate 70 stretches almost 2200 miles across the United States.

Exponent Rules

100

(n^3)^2

n⁶

200

(16s^6)/(8s^2)

2s⁴

300

(-6a^5b^4c^3)(5a^3b^4c^5)

-30a^8b^8c^8

400

Simplify completely.

(2^5*5^2*(-6)^4)/((-6)^2*2^3*5^2)

2^2*(-6)^2 = 144

500

The processing speed of a certain computer is 10¹¹

instructions per second. Another computer has a processing speed that is 10³ times as fast. How many instructions per second can the faster computer process? Write your claim as a complete sentence, restating the question.

The second computer can process 10¹⁴ instructions per second.

Negative Exponents

100

Write this expression using a negative exponent.

1/8^2

8^-2

200

Write this expression with a negative exponent.

1/49

7^-2

300

Evaluate this expression.

5^-3

1/125

400

Simplify. Express using positive exponents.

(2^-9)/2^4

1/2^13

500

A common flea that is

2^-4

inch long can jump about 2³ inches high. About how many times its body size can a flea jump? State your claim in a complete sentence, restating the question.

A common flea can jump

2^7

or 128 times its body size.

Scientific Notation

100

Write this number in scientific notation.

2,825

2.8 x 10³

200

Express this in standard notation.

3.5 x 10⁵

350,000

300

Express in scientific notation.

0.0126248

1.26 x 10^-2

400

A Petri dish contains 2.53 x 10¹¹ bacteria. Write the number of bacteria in standard form. 

253,000,000,000

500

A light year is used to measure distances in the solar system. A light year is 5,865,696,000,000. Write the number of miles in a light year in scientific notation.

5.865696 x 10¹²

Use Scientific Notation

100

Evaluate the expression and write the result in scientific notation.

(9.25 xx 10^7)-:(1.85 xx 10^4)

5.0 x 10³

200

(9.44 xx 10^9)*(2.36 xx 10^5)

2.22784 x 10¹⁵

300

(8.52 xx 10^6) - (4.03 xx 10^7)

-3.178 x 10⁷

400

(9.83 xx 10^4) + (2.19 xx 10^5)

3.173 x 10⁵

500

A music download website announced that over 

4 x 10⁹ songs were downloaded by 5 x 10⁷ registered users. What is the average number of downloads per user? State your claim in a complete sentence using part of the question in your answer.

The average number of downloads on a music website it 80.