Exponent Laws Review

Product Rule

100

Simplify:

 2x^3 * 5x^6 

10x^9

200

Simplify:

(15b^3c^7)*(2b^6c^0)*(b^-5c)

30b^4c^8

300

Simplify:

4y^3*5y^-10

20/y^7

400

Simplify:

3u^-2v^4*3u^-3

 

(9v^4)/u^5

500

Simplify:

 3a^-1b^3*a^-4*3ba^3 

(9b^4)/a^2

Quotient Rule

100

Simplify

(3bc)/(4c^3)

(3b)/(4c^2)

200

Simplify:

(3xy^-4)/(4y^4)

(3x)/(4y^8)

300

Simplify:

(2x^0y^2*3x^4y^3)/(3x^-1y^0)

2x^5y^5

400

Simplify:

(2m^-2n^3*4m^-3n^2)/(3mn^3*2m^2n^3)

(4)/(3m^8n)

500

Simplify:

(2x^4y^0)/(3x^0y^-2*4x^-2y^2)

(x^6)/6

Power Rule

100

Simplify:

(3a^3b^2)^3

27a^9b^6

or

3^3a^9b^6

200

Simplify:

(3u^0)^-4

1/81

or

1/(3^4)

300

Simplify:

(2x^4y^-4)^4*2xy^0

(32x^17)/(y^16)

or

(2^5x^17)/(y^16)

400

Simplify:

(2xy^0)/(x^4y^4*2x^3y^-4)

1/(x^18)

500

Simplify:

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

(x^10y^4)/16

or

(x^10y^4)/(2^3)

Add and Sub Polynomials

100

Simplify:

(4m+3m^2)+(4m-2m^3)

m^3+8m

200

Simplify:

(4b^4+b^3)-(b^3+5b^4)

-b^4

300

Simplify:

(-3b-6b^2+6b^3)-(-6b^2+5b^3)

b^3-3b

400

Simplify:

5(x^2-1)+2x(4x+7)

13x^2+14x-5

500

Simplify:

6(x-7)-4x(2x^2+5x-1)

-8x^3-20x^2+10x-42

Multiply Polynomials

100

Simplify:

(x+5)(x-5)

x² - 25

200

Simplify:

(x-7)^2

x^2-14x+49

300

Simplify:

(8x+6)(6x-4)

48x^2+4x-24

400

Simplify:

(4r+3)(8r+3)

32r^2+36r+9

500

Simplify:

(5x-2)(3x^2+7x-5)

15x^3+29x^2-39x+10