4.4 Simplifying Algebraic Expressions Involving Exponents Worksheet
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74.4
Simplifying Algebraic
Expressions Involving
Exponents
GOAL
Simplify algebraic expressions involving powers and radicals.
LEARN ABOUT the Math
The ratio of the surface area to the volume of microorganisms affects their ability
Surface Area/
to survive. An organism with a higher surface area-to-volume ratio is more
Radius ( m)
m
Volume
buoyant and uses less of its own energy to remain near the surface of a liquid,
4p
where food is more plentiful.
a
4
1
pb
Mike is calculating the surface area-to-volume ratio for different-sized cells. He
3
assumes that the cells are spherical.
9p
1.5
For a sphere,
4.5p
4
2
3
and
SA(r) 5 4pr
V(r) 5
.
pr
16p
3
a
32
2
He substitutes the value of the radius into each formula and then divides the two
pb
3
expressions to calculate the ratio.
25p
2.5
a
125
pb
6
36 p
3
36 p
49p
a
b
343
3.5
6p
?
How can Mike simplify the calculation he uses?
231
Chapter 4 Exponential Functions
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