Page 98 - MarceAlgebra Demystified

CHAPTER 5 Exponents and Roots 85

1 1
This property says that a is the reciprocal of a. In other words, a means
‘‘invert a.’’

Examples

1 1
1 1
2 ¼ x ¼
2 x
1 1 1
x 1 x y y 2 3 1

¼ ¼ 1 ¼ 1 ¼ ¼ ¼ 4
y x y x x 3 2 4
y
1
Property 6 a n ¼
a n
1 n 1 n n
1
This is a combination of Properties 3 and 5: ¼ ¼ a ¼ a :
a n a

Examples

1
6
5 ¼
5 6
1
10
x ¼ 10
x
3 1 ! 3
x x 3
y
¼ ¼
y y x
2 5
4 4
¼
5 2
Often a combination of exponent properties is needed. In the following
examples the goal is to rewrite the expression without using a negative
exponent.

Examples

1 1
6 2 12 7 6 1
ðx Þ ¼ x ¼ x x ¼ x ¼
x 12 x