Algebra Rules Review Sheet Page 20

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20
REVIEW OF ALGEBRA
√
√
√
3
3
93. (2x
3
3
2
4
3/2
3/2
2
3/2
4
3/2
1/2
2
3
6
2
4
y
)
= 2
(x
)
(y
)
= 2 · 2
x
y
= 2
2 |x|
(y
)
= 2
2 |x|
y
2
x
94. (x
−5
3
10
−3/5
−5
−3/5
3
−3/5
10
−3/5
15/5
−9/5
−30/5
y
z
)
= (x
)
(y
)
(z
)
= x
y
z
=
9/5
6
y
z
95.
6/5
by definition 4 for exponents.
5
6
y
= y
√
96. (
3
1/4
3
3/4
4
a )
= (a
)
= a
1
1
1
97.
−5/2
=
=
= t
√
5
1/2
5
5/2
(t
)
t
t
√
8
5/8
5
x
x
1
98.
(5/8) − (3/4)
−1/8
√
=
= x
= x
=
4
3/4
1/8
x
x
3
x
√
1/4
1/2
1/2
1/2
1/2
t
st
t
s
t
1/4
4
99.
(1/2) + (1/2)
(1/2) − (2/3)
−1/6
1/4
=
= t
s
= (ts
)
2/3
2/3
s
s
1/4
t
1/4
(−1/6) · (1/4)
= t
s
=
1/24
s
√
√
√
√
√
100.
4
4
4
4
4
2n
1/4
2n/4
n/2
2n + 1
−1
2n + 1
−1
2n + 1 − 1
2n
r
×
r
=
r
× r
=
r
=
r
= (r
)
= r
= r
√
√
√
x − 3
x − 3
x + 3
(x − 9)
1
101.
√
√
√
=
·
=
=
x − 9
x − 9
x + 3
(x − 9) (
x + 3)
x + 3
1
1
1
1
1 − x
√
√
√
− 1
− 1
+ 1
− 1
x
x
x
−1
−1
x
x
102.
√
=
·
=
=
=
=
1
x − 1
x − 1
1
1
1
x + x
√
+ 1
(x − 1)
√
+ 1
(x − 1)
√
+ 1
x
√
+ 1
x
x
x
x
√
√
√
3
x
x − 8
x
x − 8
x
x + 8
x
− 64
103.
√
√
=
·
=
x − 4
x − 4
x
x + 8
(x − 4)(x
x + 8)
2
2
(x − 4)(x
+ 4x + 16)
x
+ 4x + 16
[Equation 4 with a = x, b = 4]
=
√
=
√
(x − 4)(x
x + 8)
x
x + 8
√
√
√
√
√
√
2 + h +
2 − h
2 + h +
2 − h
2 + h −
2 − h
2 + h − (2 − h)
104.
=
·
√
√
=
√
√
h
h
2 + h −
2 − h
h
2 + h −
2 − h
2
=
√
√
2 + h −
2 − h
√
√
√
2 3 +
5
2
2
3 +
5
3 +
5
105.
√
√
√
=
·
=
=
9 − 5
2
3 −
5
3 −
5
3 +
5
√
√
√
√
x +
y
x +
y
1
1
106.
√
=
√
·
√
=
√
√
√
x −
y
x −
y
x +
y
x − y
√
√
√
2
2
2
x
+ 3x + 4 + x
x
+ 3x + 4 − x
3x + 4
107.
x
2
+ 3x + 4 − x =
x
2
+ 3x + 4 − x ·
√
=
√
=
√
2
2
2
x
+ 3x + 4 + x
x
+ 3x + 4 + x
x
+ 3x + 4 + x
√
√
√
√
√
√
2
2
x
2
+ x +
x
2
− x
x
+ x − (x
− x)
108.
2
2
2
2
x
+ x −
x
− x =
x
+ x −
x
− x ·
√
√
=
√
√
2
2
2
2
x
+ x +
x
− x
x
+ x +
x
− x
2x
=
√
√
2
2
x
+ x +
x
− x
109. False. See Example 14(b).
110. False. See the warning after Equation 10.
16 + a
16
a
a
111. True:
=
+
= 1 +
16
16
16
16
1
1
1
xy
112. False:
=
=
=
6 = x + y
x + y
1
1
−1
−1
x
+ y
x + y
+
x
y
xy
113. False.
114. False. See the warning on page 2.

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