Laws of Exponents

Multiplying

100

Express 3⁵ ∙ 3⁴ ∙ 3⁷ in simplified exponential notation.

3¹⁶

200

Simplify (5b³)(-6b⁸)

-30b¹¹

300

Simplify (ab)(-3ab)

-3a²b²

400

Simplify   (-a²)(-3a)

3a³

500

Simplify   -4x⁴ (-x⁵)(x)

4x¹⁰

Dividing

100

x/x

1

200

Simplify     -6x⁶/3x² 

^{** Remember / means division}

-2x⁴

300

Simplify    2a³bc⁵ / -abc⁴ 

*** Remember / means divide

-2a²c

400

Simplify  6ab/3ab² 

^{** Remember / means division}

What is 2/b

500

Simplify 15a³b⁴/12a³b³

 5b/4

Power to a Power/Word Problems

100

Simplify (a²)³

 a⁶

200

Simplify (-2x³)²

4x⁶

300

Simplify  (x^-5)²

x^-10 or 1/x¹⁰

400

John and Kate are both musicians who sell their songs online.  During the same year, Kate sold 4y⁵ downloads of her songs and John sold 12y⁶ downloads of his songs.  How many times greater is the number of songs that John sold than the number of songs that Kate sold?

3y

500

How many times greater is 10¹⁵ than 10¹² ? Express your answer in standard form. (No exponent)

1000 times greater

Negative Exponents

100

Express with a positive exponent x^-3

1/x³

200

Simplify and express with a positive exponent, if necessary  

b^-4b

1/b³

300

Simplify and express with a positive exponent, if necessary   

2³(2^-5)(2)

1/2

400

Simplify and express with a positive exponent, if necessary      6^-5/6³

1/6⁸

500

Simplify and express with a positive exponent, if necessary    x^-3/x^-6

x³

Zero Exponents

100

-5⁰

-1

200

2x⁰ + x⁰

3

300

(2x)⁰ + 5⁰

2

400

(-3x)⁰ - 3x⁰

-2

500

2⁰(2^-3)(2³)

1