Answers and Explanations 131
Answers
1–100
12.
z x y
z
2 2
2
+
(
)
Begin by factoring the numerator and then cancel the common factors:
x y z
x yz
x yz
x yz x y
z
x yz
z x y
z
4 3 2
2
4
2
2
2
2 2
2
2
2 2
2
+
=
+
(
)
=
+
(
)
13.
x y
z
5 17
8
For this problem, you need to know the properties of exponents. The important properties
to recall here are x
x
m
n
mn
( ) = , ( )
x
0
1
= , x x
x
m n
m n
=
+ , x
x
x
m
n
m n
=
− , x
x
n
n
−
= 1 , and 1
x
x
n
n
−
= .
Write all factors using positive exponents and then use the properties of exponents to
simplify the expression:
x y
y
z
xz
y
x y
y
x z z
x y
z
2 3
4
4
0
2
2
3
5
8 12
5
3 6 2
5 17
8
1
( ) ( )
( )
=
=
−
−
( )
14.
5 2
Factor the number underneath the radical and then rewrite the radical using
ab
a b
=
to simplify:
50
25 2
25 2
5 2
=
=
=
( )( )
15.
2 15
15
Start by rewriting the expression so it has only one square root sign. Then reduce the
fraction and use properties of radicals to simplify: