Page 94 - MarceAlgebra Demystified

CHAPTER 5 Exponents and Roots 81

Solutions

x 8
1: ¼ x 8 2 ¼ x 6
x 2
3 2
2: ðx Þ ¼ x ð3Þð2Þ ¼ x 6
7 3
3: y y ¼ y 7þ3 ¼ y 10
10
10 1
4: x x ¼ x x ¼ x 10þ1 ¼ x 11
x 3 3 2 1
5: ¼ x ¼ x ¼ x
x 2
5 5
6: ð y Þ ¼ y ð5Þð5Þ ¼ y 25
These properties also work with algebraic expressions.

Examples

2
3 5
4
(x +3) (x +3) =(x +3) 6 [(x + 11) ] =(x + 11) 15
7
ð3x 4Þ 2
¼ð3x 4Þ
5
ð3x 4Þ
2 2 2 2
Be careful not to write ð3x 4Þ as ð3xÞ 4 —we will see later that ð3x 4Þ
2
is 9x 24x þ 16.
Practice

Simplify.
2 3
ð5x þ x þ 1Þ
1: ¼
2
5x þ x þ 1
9
ð7xÞ
2: ¼
3
ð7xÞ
0
3: ð2x 5Þ ¼
6
11
4. (x +1) (x +1) =