Page 107 - MarceAlgebra Demystified

94 CHAPTER 5 Exponents and Roots

2 4 4 1 2 3 5 4 4 4 2 4 4 4 3 1 3 2 3 5 4
9: ð2xy z Þ ð3x z Þ ðxy z Þ¼½2 x ð y Þ ðz Þ Š½3 ðx Þ ðz Þ Šðxy z Þ
4 8 16 3 6 1 5 4
¼ð16x y z Þð27x z Þðx y z Þ
2 13 26
¼ 432x 4þð 3Þþ1 8þ5 16þ6þ4 ¼ 432x y z
y
z
4 3 2 4 3 4 3 4 2 4 3 12 4 8 3 16 8
2ðxy Þ ðyz Þ 2x ðy Þ y ðz Þ 2x y y z 2x y z
10: ¼ ¼ ¼
4 4 4
4 4 4 4
4 4 4
ð3xyzÞ 4 3 x y z 81x y z 81x y z
12 4
2 3 4 16 4 8 4 2 1 12 4 2 1 12 4 2y z
¼ x y z ¼ x y z ¼ y z ¼
81 81 81 x 81x
There are times in algebra, and especially in calculus, when you will need to
1 1
convert a fraction into a product. Using the fact that ¼ a , we can rewrite
a
a fraction as a product of the numerator and denominator raised to the 1
power. Here is the idea:
numerator 1
¼ðnumeratorÞðdenominatorÞ :
denominator

Examples

3 1 4 1 x n n m 1 n m
¼ 3x ¼ 4ðx þ 3Þ ¼ x ðy Þ ¼ x y
x x þ 3 y m

5x 8 3
¼ð5x 8Þð2x þ 3Þ
3
ð2x þ 3Þ

Practice

4x 2
1: ¼
y 5

2xðx 3Þ
2: ¼
ðx þ 1Þ 2
x
3: ¼
y