multiplying monomials

(3m³n²p)(4m²n⁷)

Multiply coefficents         

3 times 4 = 12

Add exponents of like variables  

m^{3 + 2} = m⁵

n²⁺⁷ = n⁹

p stays the same

ANSWER: 12m⁵n⁹p

Raising to a Power

(8x⁴y³)²

Raise coefficient to power

8² = 8 times 8 = 64

Multiplfy inside exponents and

outside power for each variable

x^{4 times 2} = x⁸

y^{3 times 2} = y⁶

ANSWER

64x⁸y⁶

Dividing Monomials

12a⁴b⁷c⁴

18a³b¹²c

Reduce the coefficient

12/18 = 2/3

Subtract exponents & put variable where higher exponent was

a^4-3 = a¹ on the top

b^{12 - 7} = b⁵ on the bottom

c^{4 - 1} = c³ on the top

ANSWER:

2a⁴c³

3b⁵

Zero Exponent

2x³y⁰

A zero exponent means that something

has been completely cancelled out.

 So y⁰ = 1.

2x³ times 1

ANSWER:

2x³