Game Development Reference
In-Depth Information
2
g. 90 ð3Þ
þ 10
h. n
2
n
30
i.
ð
a
þ
b
Þ
9
9
ða þ bÞ
r
9
s
8
r
0
s
4
j.
Things That Go Wrong
Simple uses of exponents sometimes create situations in which it is easy to make mistakes. To
investigate how this happens, begin by considering the following situation, in which you are
dealing with a sum enclosed in parentheses and then raised by the power of 3:
ð2 þ 3Þ
3
¼ 5
3
¼ 125
This solution for the problem is correct. You carry it out by first resolving the addition enclosed in the
parentheses. The result of the addition is 5. You then raise 5 to the power of 3, which results in 125.
Here are a couple of other such problems, each solved correctly:
ð2 þ 5Þ
2
2
þð2 þ 4Þ
¼ 49 þ 36 ¼ 85
ð2
2
2
2
2
2
¼ 8
2
þ 6
2
¼ 64 þ 36 ¼ 100
With both of these problems, you first attend to the operations enclosed in the parentheses before
dealing with the exponents that apply to the value within the parentheses.
þ 4Þ
þð4 þ 2Þ
¼ð4 þ 4Þ
þð6Þ
Things go wrong, however, if you inappropriately apply the distributive property to such opera-
tions. Here is the wrong approach to solving a problem:
3
¼ 2
3
þ 3
3
¼ 8 þ 27 ¼ 35 Not correct
This is not the correct approach to solving problems because you cannot distribute the operation
of the exponent across the two values in the parentheses. The parentheses make (2 þ 3) into one
expression. You must add these values before you move on to working with the power of 3.
ð2 þ 3Þ
Here is another way you can represent the problem:
3
ð2 þ 3Þ
¼ð2 þ 3Þð2 þ 3Þð2 þ 3Þ¼5 5 5 ¼ 125
In this representation of the problem, the expression in the parentheses is multiplied by itself
three times. This is what the power 3 instructs you to do. It applies to the whole expression, not to
the values in the parentheses separately.
Scientific Notation
The large numbers that characterize many scientific problems become much
easier to manage if you employ scientific notation. Scientific notation involves
taking a large, bulky number and replacing it with an expression that involves
