Properties of Exponents

Product Rule

100

x^-6*x^5*x^3

x^2

200

(3x^3y)(8x^3y^2) 

24x^6y^3

300

(3x)^3x^4

27x^7

400

(-2x^2y)(-2y^2z)(x^-2)

4y^3z

500

2x^3y^-3*2x^-1y^3

4x^2

Quotient Rule

100

4^5/4^3

16

200

(12x^8)/(3x^5)

4x^3

300

(16x^4*y^3*x^2)/(8x^3*y^2)

2x^3y

400

(36x^9x^3)/(3x^2)

12x^10

500

(2a^7b^4)/(3a^5b^-2)  

2/3a^2b^6

Power Rule

100

(x^2)^6

x^12

200

(2/5)^3

8/125

300

(s^3/t^4)^2

s^6/t^8

400

y^-8(x^2y^3)^5     

x^10y^7

500

16y^2*((3x^2)/(4y))^2

9x^4

Negative and Zero

100

5^-2

1/25

200

((x^12)^3*x^4*x^15)^0

1

300

2/x^-4

2x^4

400

((3^-1)/(2^-2))^2

16/9

500

1/x^-2*3^-3

(x^2)/27

Miscellaneous

100

2x^-2*x^2

 2

200

(x^3y^3*x^3)/(4x^2)

(x^4y^3)/(4)

300

(x^5y^2)^10

x^50y^20

400

(3a*4a^4)/(28a^2)

(3a^3)/7

500

(2a^3b^-4)/(3a^5b^-2)

2/(3a^2b^2)