Transcript Slide 1

§ 1.6
Properties of Integral Exponents
b n 
Properties of Exponents
Exponent Rules
b m  b n  b m n
Product Rule
When multiplying exponential expressions with the
same base, add the exponents.
Quotient Rule
b m mn
 b ,b  0
n
b
When dividing exponential expressions with
the same nonzero base, subtract the exponent
in the denominator from the exponent in the
numerator.
Blitzer, Intermediate Algebra, 5e – Slide #2 Section 1.6
Properties of Exponents
Exponent Rules
Examples
q3q5q 2  q352  q10
Product Rule
4a b c 3a c   4  3  a
2 3 6
4 7
2
 a 4  b3  c 6  c 7 
12a 2 4b3c 67  12a 6b3c13
Quotient Rule
z 8 83 5
z z
3
z
18r 5 q 3t 6 18 r 5 q 3 t 6
5  3 3 2 6  4





2
r
q t 
3 2 4
3
2
4
9r q t
9 r q t
2r 2 q1t 2  2r 2 qt 2
Blitzer, Intermediate Algebra, 5e – Slide #3 Section 1.6
Properties of Exponents
The Zero Exponent Rule:
If b is any real number other than 0, then
b 1
0
Negative Exponent Rule: If b is any real number
other than 0 and n is a natural number, then
1
b  n
b
n
and
1
n

b
b n
Blitzer, Intermediate Algebra, 5e – Slide #4 Section 1.6
Properties of Exponents
Exponent Rules
Examples
170  1
Zero Exponent Rule
5x y z
3
2 34
1  1
xq2 
Negative Exponent Rule
3
4
13P Q R
5

0
1
xq2
1
1 13Q 4
4
 13 3  Q  5  3 5
P
R
PR
Blitzer, Intermediate Algebra, 5e – Slide #5 Section 1.6
Properties of Exponents
Exponent Rules
Examples
4 x 3 y 6 4 y 6  pq

2
x3
 pq
2
Negative Exponents in
Numerators and
Denominators
2
 2  32  43  2  3  3  4  4  4  1152
 2 3
3 4
3 
x 4
Power Rule
d 
2 3
 34 x
 d  23  d 6 
1
d6
Blitzer, Intermediate Algebra, 5e – Slide #6 Section 1.6
Properties of Exponents
Exponent
Rules
Examples
4x y 
3
Products to
Powers

2 4
5 2a 4b6
3

   
4
3
   b 
18
 
 
4
 a 2 
a 2
 3  
b 3
b 
2
6 3
 5  23  a 43  b63 
1 12 1 5a12
 5  3  a  18  18
2
b
8b
4
Quotients
to Powers
3
 5  2 3  a  4
5 2  a b
12
4
 44  x3  y 2  256 x34  y 24  256x12 y8
2
4
 
 
 3g 3h 2   3g 3 
3g 3

  
 
2 
7 fh 2
 7 f   7 fh 
2
2

a  24 a 8
 34  12
b
b
 
f h 
32 g 3
72
2
2
2 2
9 g 32
9g 6


2 22
49 f h
49 f 2 h 4
Blitzer, Intermediate Algebra, 5e – Slide #7 Section 1.6
Simplifying Exponential Expressions
Simplification
Techniques
Examples
If necessary, remove
parentheses by using the
Products to Powers Rule or the
Quotient to Powers Rule.
2ab4  24 a4b4
3
173 173 4913
 17 
 2   2 3  23  6
x
x
x 
x
 
Q 
 Q7119  Q1349
W 
 W 510  W 50
71 19
If necessary, simplify powers to
powers by using the Power
Rule.
5 10
Blitzer, Intermediate Algebra, 5e – Slide #8 Section 1.6
Simplifying Exponential Expressions
Simplification
Techniques
Examples
H 4  H 16  H 416  H 20
Be sure each base appears only
once in the final form by using
the Product Rule or Quotient
Rule
If necessary, rewrite
exponential expressions with
zero powers as 1. Furthermore,
write the answer with positive
exponents by using the
Negative Exponent Rule
V 23
 V 2317  V 6
17
V


0
3  2 45X 3Y 4  3  2 1  5
31
12

31
K
K 12
Blitzer, Intermediate Algebra, 5e – Slide #9 Section 1.6
Properties of Exponents
Of I M P O R T A N CE to note…
Be sure you pay special attention to the
study tip on the bottom of page 72. This
tip will help you avoid common errors
that can occur when simplifying
exponential expressions.
Blitzer, Intermediate Algebra, 5e – Slide #10 Section 1.6