Pre-Algebra Demystified

SOLUTION

ð
6a^4 b^5 Þ^3 ¼ð
 6 Þ^3 a^4 ^3 b^5 ^3

¼
216a^12 b^15

EXAMPLE

Find (
xy^3 )^4.

SOLUTION

ð
xy^3 Þ^4 ¼ð
1xy^3 Þ^4

¼ð
 1 Þ^4 x^1 ^4 y^3 ^4

¼1x^4 y^12

¼x^4 y^12

PRACTICE

Find each of the following:

1. (x^4 )^5


2. (3a)^2


3. (6m^2 n^4 )^3


4. (
   5a^3 b^2 )^2


5. (7x^5 y^2 )^3

ANSWERS

1. x^20


2. 9a^2


3. 216 m^6 n^12


4. 25a^6 b^4


5. 343x^15 y^6

Multiplication of a Polynomial by a Monomial

When a polynomial is multiplied by a monomial, the distributive property is
used. Recall from Chapter 7 that the distributive property states that a(bþc)
¼abþac.

To multiply a polynomial by a monomial, multiply each term in the poly-

nomial by the monomial.

CHAPTER 12 Monomials and Polynomials 239