Beginning Algebra, 11th Edition

Using Area Formulas

Find an expression that represents the area in (a)FIGURE 1and (b)FIGURE 2.

EXAMPLE 8

OBJECTIVE 6 Use combinations of rules.

Using Combinations of Rules

Simplify.

(a)

Power rule (c)

Multiply fractions.

Product rule

or

32

9

=

25

32

,

=

22 +^3

32

=

22 # 23 32 # 1

=

22

32

#^2

3

1

a

2

3

b

2 # 23

EXAMPLE 7

300 CHAPTER 5 Exponents and Polynomials

(b)

Product rule

= 57 x^7 Power rule (b)

= 15 x 27

15 x 2315 x 24

(c)

Power rule (b) Power rule (a) Commutative and associative properties

,or Product rule; multiply.

Notice that 12 x^2 y^324 means 24 x^2 #^4 y^3 #^4 , not 12 # 42 x^2 #^4 y^3 #^4.

= 16 # 27 x^11 y^18432 x^11 y^18

= 24 # 33 x^8 x^3 y^12 y^6

= 24 x^8 y^12 # 33 x^3 y^6

= 241 x^2241 y^324 # 33 x^31 y^223

12 x^2 y^32413 xy^223

(d)

Power rule (b) Power rule (a) Product rule

= -x^21 y^14 Simplify.

= 1 - 1251 x^2121 y^142

= 1 - 1221 x^621 y^221 - 1231 x^1521 y^122

= 1 - 1221 x^322 y^2 # 1 - 1231 x^5231 y^423

= 1 - 1 #x^3 y 221 - 1 #x^5 y^423 - a=- 1 #a

1 - x^3 y 221 - x^5 y^423

NOW TRY

CAUTION Be aware of the distinction between and.

, while

OBJECTIVE 7 Use the rules for exponents in a geometry application.

12 y 23 = 2 y# 2 y# 2 y= 8 y^32 y^3 = 2 #y#y#y.

12 y 23 2 y^3

NOW TRY
EXERCISE 7
Simplify.

(a) (b)

(c) 1 x^4 y 251 - 2 x^2 y^523

a 18 k 2518 k 24

3

5

b

3 # 32

NOW TRY ANSWERS