Part II: The Answers
130
Answers
1–100
8.
5
3
3
5
2
x x
x
y
(
)
(
)
−
+
Recall that to divide by a fraction, you multiply by its reciprocal:
a b
c d
a
b
d
c
ad
bc
= ( )( ) = . After rewriting the fraction, factor and cancel the common factors:
x
x
xy
x
x
x y
x
x
xy
x y
x
x
2
3
2
3 2
2
3
3 2
2
5
6
6
3 10
10
5
6
6
10
3 10
−
+
+
−
=
−
+






+
−

 




=
−
−






+
−






=
−



(
)(
)
(
)(
)
x
x
xy
x y
x
x
x
y
2
3
6
10
5
2
3
3
3
3 2
 


+






=
−
+
5
5
5
3
3
5
2
2
x
x
x x
x
y
(
)
(
)
9.
x y z
3 2 13
Write each factor using positive exponents and then simplify. To start, notice that z
−8
in the denominator becomes z
8 when it moves to the numerator:
x y z
y z
x y z z
y
x y z
x y z
3 4 5
2
8
3 4 5 8
2
3 2 13
3 2 13
1
−
=
=
=
10.
(
)
x
x y
+
+
(
)
3
5
2
3
To simplify, cancel the common factors:
x
x y
x x
y
x
x y
+
(
)
+
(
)
+
+
(
)
=
+
+
(
)
3
5
3
5
3
5
2
4
14
6
17
2
3
(
)
(
)
11.
1
Because the entire expression is being raised to the power of zero, the answer is 1:
4
18
1
2 100
3
15 4 8
0
x y z
x y z
−





 =
There’s no point in simplifying the expression inside the parentheses.