Game Development Reference
In-Depth Information
Division with a Negative Exponent
Consider likewise the effect of dividing a number by a number that possesses a
negative exponent:
4
3
4
4
¼
4
3
4
4
¼
4
3
þ
4
¼
4
7
Dividing 4
3
by 4
4
is the same as multiplying 4
3
by 4
4
.
Negative Numbers and Exponents
When you raise a negative number to a given power, whether you raise it an even
or odd number of times makes a difference. If you raise a negative number by an
even power, then you multiply it by itself an even number of times, so the result is
positive. If you raise a negative number by an odd power, then you multiply the
number by itself an odd number of times, so the result is negative. Consider the
following expressions:
2
ð
3
Þ
¼ð
3
Þð
3
Þ¼
9
Even number power is positive
:
3
ð
3
Þ
¼ð
3
Þð
3
Þð
3
Þ¼
27
Odd number power is negative
:
4
ð
3
Þ
¼ð
3
Þð
3
Þð
3
Þð
3
Þ¼
81
Even number power is positive
:
Powers of Powers
You can raise a power by a power. In this case, you multiply one exponent by
another. Here is an example:
3
ð
2
2
¼
2
2
3
¼
2
6
Þ
¼
64
2
ð
5
2
¼
5
2
2
¼
5
4
Þ
¼
625
Powers of Zero and One
A number that possesses an exponent of 1 is equal to itself:
a
1
3
1
¼ a
¼
3
A number raised to the power of zero is equal to 1:
a
0
3
0
¼
1
¼
1
