Simplify each of the following expressions as much as possible. Express final answers with positive exponents.
1. 4x3
2
a b
5. 2 −3
b a
2. (−z)3 (3z)4
6.
3.
8. −93/2
4 −5
25p8
10p4 q
√
3
9. 3z · 32z
272
12(1 + y)5
7.
9(1 + y)3
4. 8−1/3
11. 2n3 m−1
10.
x−3 y 4
5
2
(3nm)0
2an+1
a2n−1
12.
−3
13.
a−1
ab
+ b−1
Determine a function in the form f (x) = k · bx for each of the graphs shown below.
14.
15.
16.
Determine a function of the form f (x) = k · bx , whose graph passes the indicated points.
17. (0, 2) and (4, 8)
18. (1, 12) and (3, 192)
19. Determine whether the following statements are true or false.
a) 3x2 y
b)
√
3
4
= 3x8 y 4
1
e) −1
=x+y
x + y −1
t4 = t3/4
3/2
f)
m
c) xmn = (xn )
g)
d) 2−2 = −4
c
=
d1/2
r
c3
d
1
= 3x−1
3x
h) 7 a2 − b
i) x1/3 =
√
3
=√
7
a2 − b
1
x3
j) 2x2 − 8
k)
−1/2
3
= 8 x2 − 4
−64 is undefined
3