Multiplying Monomials
Multiplying a Monomial by a Monomial
To find the product of two monomials, multiply the coefficients. Then, use
the Multiplication Property of Exponents to combine variable factors that
have the same base.
Example 1
Find: 7m^{3}n^{4} Â· 6mn^{2}
Solution
Write the coefficients next to each other.
Write the factors with base m next
to each other, and write the factors
with base n next to each other. 

7m^{3}n^{4} Â· 6mn^{2}
= (7 Â· 6)(m^{3} Â·
m^{1})(n^{4} Â· n^{2}) 
Use the Multiplication Property of
Exponents.


= (7 Â· 6)(m^{3 + 1})(n^{4
+ 2}) 
Simplify. 

= 42m^{4}n^{6} 
Remember:
Multiplication Property of Exponents:
x^{m} Â· x^{n} = x^{m + n}
Example 2
Find:
Solution
Write the coefficients next to each other.
Write the factors with base w next
to each other, and write the factors
with base y next to each other. 

Use the Multiplication Property
of Exponents.


Simplify. 
= 2w^{5}x^{7}y^{6} 
Example 3
Find: (5x^{3}y)(3x^{5})(2xy^{5})
Solution
Write the coefficients next to
each other.

(5x^{3}y)(3x^{5})(2xy^{5}) 
Write the factors with base x
next to each other and write
the factors with base y next to
each other. 
= (5 Â· 3
Â· 2)(x^{3}
Â· x^{5}
Â· x^{1})(y^{1}
Â· y^{5}) 
Use the Multiplication Property
of Exponents.
Simplify. 
= (5 Â· 3
Â· 2)(x^{3}
^{+ 5 + 1})(y^{1 + 5})
= 30x^{9}y^{6} 
