Download Powerpoint Lesson 1.1.2

Rational and Irrational
Numbers and Their
Properties (1.1.2)
September 7th, 2016
Solving Exponential Equations
General
Power
a
a
a
x ab
a
Rational
Exponent-Case
1
Rational
Exponent-Case
x 3  64 
x b x  b
a
Root
Example
x b
 x  b
a
a
4
a
x  3
 x  ba
x
m
n
x
n
 
b x
m gn
n m
x b
m
b
m
n
n
n
m
 
n
x
m
n
m
b
n
x
m
xb
n
2
 27 
m
 bn  x m  bn
 m x m  m bn  x  m bn
3
2
x 3  27 
4
Ex. 1: Simplify
n 5 n
2
3
.
Why does it make sense to add the exponents
when multiplying variables of the same base?
a
Ex. 2: Simplify
a
3
4
2
5
.
Why does it make sense to subtract the
exponents when dividing variables of the same
base?
Ex. 3: Solve the equation x  36
3
2
.
Ex. 4: Solve the equation x
53
2
.
How can you determine whether the sum or
product of two numbers will be rational or
irrational?
Ex. 1: Are the following sums and products
rational or irrational?
a)
c)
e)
1 3

2 4
0.3b)
 0.75
3 5

4 6
1
 2
2
0.1d) 0.25 
5
g)  3
2
4 f) 5
2 h)3
Do you see any pattern in what makes the result
rational or irrational?
RULE
EXAMPLE
Rational + Rational =
Rational
1
3
0.25   0.75 
2
4
Rational x Rational =
Rational
1
1
0.25   0.125 
2
8
Rational + Irrational =
Irrational
1
1
 3  3
2
2
Rational x Irrational =
Irrational
3 2
 3
   2 
4
4
Is the sum or product of two irrational numbers
always irrational?
Ex. 2: Are the following sums and products
rational or irrational?
a)
c)
34 3
2 8
2 b)3 7  3 7 
2 d)5