4.4 Simplifying Algebraic Expressions Involving Exponents Worksheet Page 7
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1
2
3
4
5
6
7Evaluate. Express answers in rational form with positive exponents.
8.
( "10 000x)
3
for
x 5 16
a)
2
a
3
4
b
20.5
(4x
)
b)
for
x 5 5
3
6
(x
)
" 25a
2
23
4
6
(22a
b)
a 5 1,
b
c)
for
b 5 2
2
2
25
(18m
n
) (32m
n)
d)
Ä
for
m 5 10,
n 5 1
23
4mn
Simplify. Express answers in rational form with positive exponents.
9.
! 64a
2
a
b
12
3
4
6
0.5
12
8
0.25
(36m
n
)
(81m
n
)
a)
c)
1.5
26
(a
)
1
21
2
b
0.5
a
3
2
3
b
a
18
(6x
)
(6y
)
(x
)
3
6
! 243x
b)
d)
5
6
10
(9xy)
1
8
24
(16x
y
)
4
If
M 5
, determine values for x and y so that
10.
22
8
32x
y
T
M , 0
M 5 1
M . 1
0 , M , 1
a)
b)
c)
d)
The volume and surface area of a cylinder are given, respectively, by the
11.
A
formulas
2
2
and
V 5 pr
h
SA 5 2prh 1 2pr
.
a) Determine an expression, in simplified form, that represents the surface
area-to-volume ratio for a cylinder.
b) Calculate the ratio for a radius of 0.8 cm and a height of 12 cm.
If
x 5 22
and
y 5 3,
write the three expressions in order from least to
12.
greatest.
2
24
23
23
23
21
22
y
(x
)
y
x
( y
)
5
2
25
22
23
24
,
, ( y
) (x
)
( y
) (x
)
25
24
2
25
4
x
( y
)
(x
) ( y
)
How is simplifying algebraic expressions like simplifying numerical ones?
13.
C
How is it different?
Extending
4
3
a) The formula for the volume of a sphere of radius r is
V(r) 5
p r
.
14.
3
Solve this equation for r. Write two versions, one in radical form and one
in exponential form.
256p
3
b) Determine the radius of a sphere with a volume of
m
.
3
! x(x
2n11
)
! x
, x . 0.
Simplify
15.
3
3n
Chapter 4 Exponential Functions
237
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