Exponent Rules

Product Rule

100

x^3 * x^6

x^9

200

2x^5 * x^7

2x^12

300

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

24f^12

400

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

16/r^2

500

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

(21s^11)/p^2

600

(2/3)^(1/3)*(2/3)^(1/4)

What is 

(2/3)^(7/12)

Power Rule

100

(x^4)^5

x^20

200

4(y^3)^2

4y^6

300

(xy)^6

x^6y^6

400

(4w^5)^2

16w^10

500

(8w^3y^7)^0

1

600

(6x^(1/2)y^(2/3))^(1/5)

What is 

6^(1/5)y^(1/10)x^(2/15)

Quotient Rule

100

x^7/x^3

x^4

200

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

2x

300

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

2x^7

400

u^2/u^9

1/(u^7)

500

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

1/(2m^4)

600

(2/3)^(1/4)/(2/3)^(1/3)

What is 

1/(2/3)^(1/12)

Negative Exponent Rule

100

Any number to the Zero power is? ___________

The base cannot be 0

What is 1

200

4x^-9

4/(x^9)

300

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

What is

(w^12y^6)/(z^10x^4)

 

400

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

18/(x^4)

500

(v^5)^-8

1/(v^40)

600

11a^2 * 3a^-6

33/a^4

Mixed Rules

100

Simply

(x^4 )^(-3)∙2x^4

What is

2/(x^8)

200

Simply

x/(2x^0 )^2 

What is

x/2

300

Simplify 

2x^2 y^4∙4x^2 y^4∙3x∙3x^3 y^(-2)

What is

72x^8y^6

400

Simplify

(2m^(-4))/(2m^(-4) )^3 

What is 

2m^8

500

Simplify

(9x^4 y^(-4) z^(-3))/(3x^2 y^(-3) z^4 )

What is 

(3x^2)/(z^7y)

600

Simplify

(3x^3 y^(-1) z^(-1))/(x^(-4) y^0 z^0 )

What is 

(3x^7)/(yz)