Properties of Exponents

Product and Quotient of Powers

100

Simplify (2²) (2⁵)

128 or 2⁷

200

Simplify:

(6^8)/(6^6)

6²

300

Simplify (r³s⁴) (s²t²)

r³s⁶t²

400

Simplify:

(6a^10)/(3a^7)

2a³

500

Simplify:

 (4⁵e⁴f³) (e⁶f)

4⁵e¹⁰f⁴

Power of a Power

100

Simplify (4²)²

256 or 4⁴

200

Simplify (u¹¹)¹¹

u¹²¹

300

(3q¹⁰)⁴

3⁴q⁴⁰

400

Simplify, express with positive exponents

 (x^-18)³

 1/x⁵⁴

500

Simplify: 

(4rs⁸)⁴

4⁴r⁴s³²  or 256r⁴s³²

Power of a Product

100

Simplify (a³b⁶)⁴

a¹²b²⁴

200

Simplify (3ab)²

3²a²b² or 9a²b²

300

Simplify (df)² (d³f)⁵

d¹⁷f⁷

400

Simplify (p⁵r⁷)⁹

p⁴⁵r⁶³

500

Simplify (2x³y)⁴

2⁴x¹²y⁴ or 16x¹²y⁴

Negative

100

simplify 4^-2

1/16

200

simplify x^-6

1/x⁶

300

2x³*2x^-3

4

400

Write using positive exponents   3d^-5

3/d⁵

500

Evaluate x^-3  when x=2

1/8

Multiple Properties

100

(2x³)⁴ * x⁶

2⁴x¹⁸ or 16x¹⁸

200

5x²y * (x⁴y³)²

5x¹⁰y⁷

300

Simplify:(4x²y³z)² * x

16x⁵y⁶z²

400

Simplify:

(16x^2y^-1)/(-4x^-1)

(-4x^3)/y

500

Simplify 

(6x^-12*4x^3y)/(-2x^^-1)

(-12y)/(x^8)