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

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

What is 

(2/3)^(2/3)

Power Rule

100

(x^4)^5

x^20

200

4(y^3)^2

4y^6

300

(4w^5)^2

16w^10

400

(xy)^6

x^6y^6

500

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

(-16y^6)/(x^6)

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

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? (Given that the base is not 0)

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

Scientific Notation

100

Write in Standard Form

4.67 x 10³

4670

200

Write in Standard Form

6.102 x 10^-2

0.06102

300

Write in Scientific Notation

93400

9.34 x 10⁴

400

Write in Scientific Notation

0.0023

2.3 x 10^-3

500

Write in Standard Form

3.06 x 10⁸

306,000,000

600

Write in Scientific Notation

0.0000000243007

2.43007 x 10^-8

Mixed

100

a^m*a^n=

a^(m+n)

200

a^(-n)=

1/a^n

300

(-2)^3

a. 8

b. -8

c. 

(1)/(8)

d. 

(-1)/(8)

b. -8

400

(ab)^n

a^nb^n

500

Expand the following: 

3^3x^3y^2

3*3*3*x*x*x*y*y

600

Expand the following: 

(2*5)^3

(2*5)*(2*5)*(2*5)