Chapter 5 e X P O N e N T S a N D r O O T S 111

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

✔SOLUTIONS

1. x
   y

x

y

x

y

y

x

x

y

(^3) y
2
(^5235)
25
2
2
15
10
^2










 =⋅=⋅
− ()
() xx
xy xy x
(^2) y
152210 13 8 13
=== 8
−− −

2. ()
   ()

()()

()()

2

6

2

6

(^35416)
532
43454
25232
xy^12
xy
xy
xy
==x yy
xy
xy
xy xy
20
10 6
12 10 206
214 214
36
16
36
4
9
4
9

==
−−

3. () 23 xx^32 ()−−^13 ==[( 2323 xx)]^23 [(^13 )]() 42 xx^63 () 7 −
   = 1108 xx^63 +−()= 108 3


4. () 31 () 23 (())(( 12 ))
   1
   9

xy^42 xy^2222 xy^4222 xy^22

x

−−= −−

= −−− −+ −+

−









=

==

28 42 2482

26

144 144

9

16 16

yxyxy

xy

()

xx

y

x

y

2

6

2

6

(^11) = 6

5. () 42 xy−−^1224 ()xy^53 =[( 4221 xy−−)(^22 )]^23 [(xy^43 )(^5 )^33
   24 12 15 212415
   10

16 8 128

128

]

==()()

=

xy−− xy xy−+ −+

xy^111

6. ()
   ()

()()

()

5

15

5

15

(^433125)
52
34333
2252
xy^12
xy
xy
xy
==xy^99
210
122910 10 1
10
225
125
225
5
9
5
9
15
xy
xy xy
x
y

=⋅=
−− −
xx
y
10
9

7. ()
   ()

()()

()

9

6

9

6

(^23281)
23
22232
3323
xy^46
xy
xy
xy
−−==xy−
2216
81
216
3
8
3
8
1 1 3
8
36
43 66
70
77
xy
xy
xy
xx

==⋅⋅=
−− −
−

8. [( )][( )] [(())][( )]
   [

93239323

81

xx++^2232 =+xx^2233 +

= (()][()]()

()

xx x

x

++=+

=+

383 648 3 +

648 3

43 43

7

9. () 23 xy^24 zx^41 ()−−zx^23 ()yz^54 =[( 2344 xy^24 )(z^44 )][(^3 xxzxyz
   xyzxzxyz

−

= −

13 23 54

16 4816 27 36 154

)( )]()

()()())

== 432 xy^43 +− ++()^1851 zx^664 ++ 432 21 yz^326