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: 7m3n4 · 6mn2
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. |
|
7m3n4 · 6mn2
= (7 · 6)(m3 ·
m1)(n4 · n2) |
| Use the Multiplication Property of
Exponents.
|
|
= (7 · 6)(m3 + 1)(n4
+ 2) |
| Simplify. |
|
= 42m4n6 |
Remember:
Multiplication Property of Exponents:
xm · xn = xm + 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. |
= 2w5x7y6 |
Example 3
Find: (-5x3y)(3x5)(2xy5)
Solution
| Write the coefficients next to
each other.
|
(-5x3y)(3x5)(2xy5) |
| Write the factors with base x
next to each other and write
the factors with base y next to
each other. |
= (-5 · 3
· 2)(x3
· x5
· x1)(y1
· y5) |
| Use the Multiplication Property
of Exponents.
Simplify. |
= (-5 · 3
· 2)(x3
+ 5 + 1)(y1 + 5)
= -30x9y6 |
|
