Intermediate Algebra – Student Workbook – Second Edition 2013

Lesson 6a - Exponents and Rational Functions
Mini-Lesson
NEGATIVE EXPONENTS
If a 0 and n is a rational number, then a
EXAMPLES: Rewrite the expressions using only positive exponents.
a) 4 1 1
3
4
3 81
b)
3 1 1 1
2x
3 3 3 3
2x 2 x 8x
c)
1
x
1
x
1 4
d) x
4
x
e) 3y
2
y
2 3
5
( 3)
(
5)
8
f) ( x )( x ) x x
8
x
3 1
n
1
n
a
POWER TO A POWER
EXAMPLES:
a) 3 2
( ) 3 = 3 6 = 729
( ) 5 = x 15
b) x 3
a
2 3 6 1
a
a
c)
6
If a is a real # and m and n are rational #’s, then
POWER OF A PRODUCT
If a and b are real #’s and n is a rational #, then
EXAMPLE:
a) (x 2 y 3 ) 4 = (x 2 ) 4 (y 3 ) 4 = x 8 y 12
b) (-2a 5 ) 3 = (-2) 3 (a 5 ) 3 = -8a 15
c) (3x -3 ) 4 = 3 4 (x -3 ) 4 = 81x -12 = 81
x 12
(ab) n = a n b n
(a m ) n = a mn
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