Lesson 4A Monomials 177

Multiply Powers

Find 7^3 · 7. Express using exponents.

73 · 7 = 73 × 71 7 = 71 Check 73 · 7 = (7 · 7 · 7)(7)

= 73 +^1 The common base is 7. = 7 · 7 · 7 · 7 or 7^4 ✓

= 74 Add the exponents.

Simplify. Express using exponents.

a. 53 · 54 b. (^) ( (^12) ) 2 · (^) ( ^1
2
(^) ) 9
A monomial is a number, variable, or product of a number and one or
more variables. Monomials can also be multiplied using the rule for
the product of powers.
Multiply Monomials
Find each product. Express using exponents.
x^5 · x^2
x^5 · x^2 = x^5 +^2 The common base is x.
= x^7 Add the exponents.
(- 4 n^3 )(2n^6 )
(- 4 n^3 )(2n^6 ) = (- 4 · 2)(n^3 · n^6 ) Use the Commutative and Associative Properties.
= (-8)(n^3 +^6 ) The common base is n.
= - 8 n^9 Add the exponents.
Simplify. Express using exponents.
c. - 3 m(- 8 m^4 ) d. 52 x^2 y^4 · 53 xy^3
You can also write a rule for finding quotients of powers.
2
6
_
21
= __^2 ·^2 ·^2 · 2 ·^2 ·^2
2
1

2 · 2 · 2 · 2 · 2 · 2
__
2
Divide out common factors.
1
= 25 Simplify.
Compare the difference between the original exponents and the
exponent in the final quotient. This relationship is stated in the
following Key Concept box.
6 factors
1 factor
5 factors
Common Misconception Common Misconception
When multiplying powers,
do not multiply the bases.
32 • 3^4 = 3^6 , not 9^6.
Properties
Commutative Property of
Multiplication
a · b = b · a
Associative Property of
Multiplication
(ab)c = a(bc)
176_189_C3L4_895130.indd 177 12/31/09 12:49 PM