Exponent And Radical Expressions Worksheets With Answer Keys Page 4
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1
2
3
4
5
6Combining to a Predefined Common Base
kx
kx
Rewrite each expression in the form 2
or 3
for a suitable k.
1
x
x
x
a) 27
b) ( 2)
c) (
)
8
x/2
4x/3
2x/3
d) 9
e) 8
f) 27
x
x
5x/4
1
x
2x
5x/2
g) 7
14
;
h) 2
(
)
i) 3
3
2
3x
2x
2/5
1/2
4
x/9
1/4
3/4
3x
j) (2
2
)
k) (9
9
)
l) (16
16
)
2x
m) Find a number b such that the function f (x) = 3
can be written in
x
the form f (x) = b
.
x/3
x
n) Find b so that the function 8
= b
for all x.
Solve the following equations for x. (x should be an integer or rational.)
2x
2
2x+1
5
a) 5
= 5
b) (2.5)
= (2.5)
1 x
5x
c) 10
= 100
d) 3(2.7)
= 8.1
x+1
3
2
3x
5x
e) (2
2
)
= 2
f) 2
= 4 2
3x
1/3)x
3x
x
4x
2x
x
(1/4)x
(1/2)x
2x
Answers a) 3
; b) 2
; c) 2
; d) 3
; e) 2
; f) 3
; g) 2
; h) 2
; i) 3
; j) 2
; k)
x
6x
3
; l) 2
; m) b = 1/9; n) b = 1/2;
Answers a) x = 1; b) x = 2; c) x =
1; d) x = 1/5; e) x = 5/2; f) x =
1;
4
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