Transcript Slide 1

Warm up
Use the laws of exponents to simplify the following.
Answer should be left in exponential form.
1.(2 )(2 ) 
4.(6  7 ) 
2.(4 ) 
513
.

2
3 2
3
2
0
3
2
35
. 
6
6. 7 
6
3 5
The laws you used in the warm up with integer bases
apply to all bases, even variable bases.
The laws also apply for all types of exponents, including
fractions and decimals.
Let’s review the rules
and see them applied.
Labeling an exponential expression
5
X
• The expression is written and read as X to the 5th
•
•
•
•
•
power.
X is called the base of the expression.
5 called a power or exponent for the expression.
The exponent, 5, tells us that we want X multiplied
with its self 5 times
Power or exponential form is X5
x  x  x  x  x is Expanded form
Practice
 Identify the base of
 Identify the exponent of
 Is
in exponential or expanded form?
ZERO POWER RULE
Any base(s) raised to the zero power will always
equal 1.
Examples
1234  1
0
9 0
( 23w gy )  1
2 .8
F2 x I  1
G
J
H7 x K
1
0
6
4
Practice
Product of Powers
When two bases are multiplied we add the exponents of
the bases.
Examples
2
3
23
5
( w )( w )  w
1
2
1 4
(my )( y )(m )  (m
3
3
4
)( y
w
1 2
3 3
)m y m y
5
1
5
If there are numbers in the expression we can multiple
them.
Example
4
6
46
10
(3r )(5r )  (3  5)(r
)  15r
Practice
Power of a Power
When we have an exponent raised to an exponent we
multiple the exponents.
Example
(a 3 ) 3  a 9
If there are numbers or more than one variable, inside the
parenthesis, they all get raised to the outside power. When
we have we first simplify by ‘distributing’ the outside
exponent inside, and then, since the two groups are
multiplied, we added the exponents of like bases.
Examples
4 3
13 43
3 12
12
(2a )  2 a
 2 a  8a
(a8 g 3 ) 2  a82 g 32  a16 g 6
42
(1 j )  (1) ( j )  1( j 8 )  ( j 8 )
4 2
2
(2 y5m) 3 ( y 3 ) 2  (23 y15m3 )((1) 2 y 6 ))  8 y 21m3
Warm up 3-2
Use the laws of exponents to simplify the following.
Answer should be left in exponential form.
6 3 5
3
4.(2h j ) 
2.( y ) 
4
5.

5/ 3
0
5( 13x y )
1.( x )( x ) 
1/ 2
3 4
8
3.z
6

2 1
x y z
6. 7 9 4 
x y z
Quotient of Powers
When dividing with exponents we subtraction the
exponents of common bases.
5 8
5
v
w
2 5
Examples r 2  r 3

v
w
3 3
v w
r
If there is no other base for you to divide with it is kept
in the same place.
Examples 3 y 7
2 8
y3
42 e2 w
2 4 1

4
e w
2 6
we
 3y 4
g w
2 5

g
w
3
w
(e 2 w) 3
e6 w3
0


e
ww
2 6
2 6
we
we
Practice
Power of a Quotient
When we raising a fraction to a power, we can rewrite the
fraction by raising everything on top by the outside
exponent and everything on bottom to the outside
exponent.
Examples
F
w I (w )

G
J
Hw K (w)
2
2
2 2
2
w4
 2  w2
w
F
2 w I (2 w )

G
J
Hgw K ( gw )
8
4
3
8 3
4 3
2 3 w24 8w12
 3 12  3
g w
g
Practice
Negative
Exponents
If we have a negative exponent we can write it as a positive by
taking the reciprocal.
If the negative exponent is on the top of a fraction we can
write it positive by simply moving it to the bottom of the
fraction.
If the negative exponent is on the bottom of a fraction we can
write it positive by moving it to the top of the fraction.
Examples
x 2 
1
6

g
g 6
1
x2
3e 2
3
 5 2
5
2g
2g e
3
6

3
g
g 6
3
3g 7

7
2g
2
Practice
Radicals and Exponents
Fraction powers can be written as radicals, roots.
Practice