4.4 Simplifying Algebraic Expressions Involving Exponents Worksheet Page 2
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Representing the surface area-to-volume ratio
EXAMPLE
SA(r)
4
2
3
Simplify
,
given that
SA(r) 5 4pr
and
V(r) 5
.
pr
3
V(r)
Bram’s Solution
SA(r)
I used the formulas for SA and V
and wrote the ratio.
V(r)
The numerator and denominator
have a factor of
so I divided
p,
both by
p.
I started to simplify the expression
by dividing the coefficients.
1
2
a4 4
4pr
4
3
5 4 3
5 3b
5
3
4
4
3
pr
3
1
The bases of the powers were the
21
same, so I subtracted exponents to
5 3r
simplify the part of the expression
involving r.
3
5
r
I used a calculator and substituted
r 5 2
in the unsimplified ratio first
and my simplified expression next.
Each version gave me the same
answer, so I think that they are
equivalent, but the second one
took far fewer keystrokes!
Reflecting
How can you use the simplified ratio to explain why the values in Mike’s
A.
table kept decreasing?
Is it necessary to simplify an algebraic expression before you substitute
B.
numbers and perform calculations? Explain.
What are the advantages and disadvantages to simplifying an algebraic
C.
expression prior to performing calculations?
Do the exponent rules used on algebraic expressions work the same way as
D.
they do on numerical expressions? Explain by referring to Bram’s work.
232
4.4 Simplifying Algebraic Expressions Involving Exponents
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