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

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

(4y^7)/(x)

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)

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)

Combining Like Terms

100

(3x +1) + (2x + 8) 

5x + 9

200

(3x + 1) - (2x + 8)

x - 7

300

(3x + y + 11) + (2xy + 10)

3x + y + 2xy + 21

400

(5x² - 1 + 2x) - (5 + 4x - x²)

6x² - 6 - 2x

500

(5x²-1 + 2x) - (5 + 4x - x²) + (3x - 2x²)

4x² - 6 + x

Distribute

100

5x(3x + 2)

15x² + 10x

200

-5x(3x² + 2x - 1)

-15x³ - 10x² + 5x

300

(4x +1)(4x -1)

16x² - 1

400

(2x² + 4)(3x +1)

6x³+2x²+12x +4

500

(2x² + 4)(3x +1 - 10y)

6x³+2x²+12x +4 -20x²y -40y