Rules of Exponents

Power rule

100

(X^a)^b

(X^ab)

200

(8⁴)³

8¹²

300

(4r³  s⁷)³

(4³r⁹  s²¹)

400

(-2m⁵)²•m³

4m¹³

500

(7²w³)⁸  (2w²)²

(14¹⁸w²⁸)

Quotient rule

100

X^a/x^b

X^a-b

200

27x⁵/42x

9x⁴/14x

300

12⁶/-6⁹

-2^-3

400

400m⁶/20m⁴

20m²

500

-18a⁸/2a³ • 5a²

9a⁵ • 5a²​

-45a⁷

​​​

Negative exponents

100

X^-a=

1/x^a

200

-5x^-2

-5/x²

300

 8k^-6

8/k⁶

400

(4r²)^-5

-1024r^-10

-1024/r¹⁰

500

-30y⁶r^-5/5y⁶r²

-6y/r⁷

Product rule

100

x^a•x^b=

X^a+b

200

H^2•h⁶

h⁸

300

-2m⁶ • 3m⁹

-6m¹⁵

400

8m⁶n⁷ • 4mn⁴ + 5m⁹n²

37m¹⁶n¹³

500

(-2m⁵)²•(7a³b)

-14a⁵b²

Adding and subtracting monomials

100

6w²+11w²

17w²

200

9x²y-10x²y

1x²y

300

-2x¹³y⁶- 8x¹³y⁶

-10x¹³y⁶

400

12xyz+14x-8xy+1xyz-2x

13xyz+12x-8xy

500

The rule for adding and subtracting monomials

What is do not change common variables and exponents