Game Development Reference
In-Depth Information
expression with relation to multiplication:
a
m
a
n
¼ a
mþn
2
2
2
4
¼
2
2
þ
4
¼
2
6
¼
64
Both of the terms provide 2 as a base. Given this situation, as long as you express
the numbers you are working with using the same base terms, you can add the
exponents to carry out the multiplication.
What if the bases are not the same? If you start with numbers that differ, you can
in many cases change them so that they represent the same base. Consider this
example:
2
2
4
2
¼
2
2
2
4
¼
2
2
þ
4
¼
2
6
¼
64
In the first expression, the bases 2 and 4 are not the same. However, 4 = 2
2
and
4
2
¼
2
4
. By manipulating the base, you can create an expres-
sion that allows you to add the exponents to carry out the multiplication.
¼
2
2
2
2
¼
2
2
þ
2
Division
If you are working with the same base number and you divide one base number
by the other, then you can subtract one exponent from the other. Consider the
following:
a
m
a
n
¼ a
mn
2
4
2
2
¼
2
4
2
¼
2
2
¼
4
Alternatively, to test the relationship, do the multiplication for each term:
2
4
2
2
¼
16
4
¼
4
When you multiply a number that has a positive exponent by a number that has a
negative exponent, you create a situation characterized by division. Here is such a
situation:
a
n
b
n
1
b
n
¼
a
n
b
n
¼ a
n
4
9
In this instance, in the lower example, the negative exponent turns 3 into
3
. At the
same time, 3 is still raised to the power of 2, so you see
1
3
2
¼
4
1
3
2
¼
2
2
3
2
¼
2
2
3
2
or
9
. The first term, 2,
1
possesses a positive exponent, and 2
2
¼
4
:
