EXPONENTIAL AND
LOGARITHMIC FUNCTIONS
Real Exponents
Scientific Notation


A number is in scientific notation when it is in the
n
form a x 1 0 w he re 1 ≤ a ≤ 1 0 a nd n is a n inte g er.
4
1. Write 9.4 X 10 in standard form
Solution: .00094
2. Write 784,000,000 in scientific notation form.
8
Solution: 7.84 X 10
Properties of Exponents
Example # 1
Evaluate each expression
FG 3 IJ
3

3
1.
2. H 4 K

4
7
36
Solutions:
1. 3
5
2.
4
3
1
Simplifying Expressions



Simplify each expression.
1.
cs t h
4 7 3
Solutions:
1. s12 t21
x
2
y
5
2. c x h
2
2.
y
x
5
6
4
Rational Exponents
Expressions with rational exponents


The properties of exponents are still valid.
b = n b for a ny rea l num b e r b ≥ 0 a nd a ny
integer n>1. This also holds when b<0 and n is odd.
1
n
1
4

Evaluate 625
1
4 4
Solution 5 = 5
c h
1
2
Evaluate 3 x 21
1
2
1
2
1
2
1
2
= 3 x 3 x 7 =3
7
When the exponent is odd


Remember when the exponent is odd, we need to
use an absolute value because we can not have
negative values. If we did, it would result in complex
numbers.
Example: Simplify r 7
3
= |r| r
Example # 2



Simplify r 9 s 5 t 2 4
Solution: r 4 s 2 t st
1 2
4
5
Solve 616 = x -9
4
625 = x 5
5
4
5
4
5
4
(625) = (x ) raise each side to the
3125 = x
5
4
power
Irrational exponents

A calculator can be used to approximate the value
of an expression with irrational exponents. For
3
ex a m p le, 2 ≈ 3 .3 2 1 9 9 7 0 8 5 .
HW # 25
Section 11-1
Pp. 700-702
#20-30 all, 33-43 odds,
75,80
