Game Development Reference
In-Depth Information
Worked Problems with Exponents
Here are a few worked problems. Study them to prepare yourself for the next
section.
x
6
x
5
x
3
x
11
x
3
¼ x
11
þ
3
¼ x
14
¼
In this example, you face the problem of first adding the exponents on the top of
the fraction. Then, on the bottom, you have a negative exponent, so you divide by
1
x
3
, which is the same as multiplying by
x
3
.
x
2
y
3
z
4
x
7
y
1
x
2
y
3
z
4
x
7
yz
8
¼
x
2
y
3
z
4
x
2
y
3
z
4
z
8
x
7
y
1
¼
x
2
y
3
z
8
y
2
z
4
x
5
x
7
y
1
z
4
¼ x
5
y
2
z
4
x
7
y
z
8
¼
z
8
¼
¼
The key here lies in recognizing the need to deal with the two negative exponents.
After you have created fractions that remove the negative signs, you can then
carry out the divisions. You invert the bottom fraction, placing
z
8
on the top of
the fraction. In the end, to remove the negative exponent from the top (
x
5
), you
end up with a fraction.
7
ðx
2
þ y
2
Þ
7
3
7
þ
3
10
Þ
3
¼ðx
2
þ y
2
ðx
2
þ y
2
¼ðx
2
þ y
2
¼ðx
2
þ y
2
Þ
Þ
Þ
Þ
ðx
2
þ y
2
This problem presents difficulties because it anticipates work with polynomials,
which receives attention in the next chapter. You cannot reduce an expression
like (
x
2
þ y
2
) without factoring it, so to work with it in this context, you treat it
as a single term.
Exercise Set 3.1
Simplify these problems involving exponents:
a. 7
2
ð6 þ 3Þ
b. 2ð5
2
Þþ2
2
c. 6
2
ð1
2
Þð1Þ
d.
ð8
2
þ 7Þð1Þ
2 þ 1
2
ð2
2
4
0
e.
Þ
3
2
2
f.
2
3
