Exponent Rules

Product Rule

100

x^3 * x^6

x^9

200

2x^5 * x^7

2x^12

300

(8r^5)(2r^-7)

16/r^2

400

(4f^8)(6f^4)

24f^12

500

(7s^5p^3)(3s^6p^-5)

(21s^11)/p^2

600

q^(1/3)*q^(1/3)

q^(2/3)

Power Rule

100

(x^4)^5

x^20

200

(y^3)^2

y^6

300

(4w^5)^2

16w^10

400

(xy)^6

x^6y^6

500

(4x^2y^3)^3

(64x^6y^9)

600

(x^(1/2)y^(2/3))^(1/5)

 

y^(1/10)x^(2/15)

Quotient Rule

100

x^7/x^3

x^4

200

(2x^6)/(x^5)

2x

300

u^2/u^9

1/(u^7)

400

(8x^10)/(4x^3)

2x^7

500

(4m^4)/(8m^8)

1/(2m^4)

600

(10x^2y^3)/(-5xy^7)

(-2x)/(y^4)

Zero and Negative Exponent Rule

100

Any number to the zero power is..? 

1

200

x^-9

1/(x^9)

300

(v^5)^-8

1/(v^40)

400

((x^2y^(-3))/(z^-5w^6))^0

1

500

(3x^-8)(6x^4)

18/(x^4)

600

11a^2 * 3a^-6

33/a^4

Mixed Rules

100

2a^3*7a^10=

14a^13

200

(3x^-2)^(4)=

81/x^8

300

(-2)^-3

b. 1/-8

400

((2y^4)/(x))^8

(256y^32)/(x^8)

500

 

(3x^3y^2)^2(4xyz)

36x^7y^5z

600

(2x^3v^-2)^3

(8x⁹)/(v⁶)