Laws of Exponents

Adding & Subtracting Monomials

100

3x + 5x - 4

8x - 4

200

-5 + 3y - 8y = 

-5y - 5

300

10m^2n + 2n - 7m^2 - 7m^2n

3m^2n+2n-7m^2

400

Find the difference of 3x and 10x

-7x

500

1/5d^4k^3+4-1/2d^4k^3=

-3/10d^4k^3+4

Product Rule

100

w^3 xx w^5

w^8

200

(3t^8)(2t^2)

6t^10

300

(2y^4)(y^3)(3y^2)

6y^9

400

(3/4mn)(8m^2n)

6m^3n^2

500

-1/3(10wv^3)(3w^2v)

-10w^3v^4

Power Rule

100

(y^3)^9

y^27

200

(j^8k^5)^3

j^24k^15

300

(-4w^3)^2

16w^6

400

-3(3c^3)^2

-27c^6

500

(1/2x^4y^2z^6)^3

1/8x^12y^6z^18

Quotient Rule

100

Using the quotient rule: 

x^a/x^b=

x^(a-b)

200

f^9/f^2

f^7

300

(100x^10)/(10x)

10x^9

400

(-18x^4y^5z)/(3xy^4)

-6x^3yz

500

((2pq)(3p^2q^4)) / (-6pq^5)

-p^2

Negative Exponents/ Zero Exponents

100

x^-6

1/x^6

200

1/w^3

w^-3

300

r^0

1

400

-5x^-5y^5   

(-5y^5)/x^5

500

(6x^5y^-4)^-2

(y^8)/(36x^10)