Transcript the exponents. - Cloudfront.net

The exponent indicates the number of
times the base is used as a factor.
EXPONENT
BASE
= 2x2x2x2x2 =32
Zero Exponents
Any number raised to the zero power
equals one!
Ex)
10
0
Ex)
=1
0= 1
1
Ex)
0
729 = 1
Another important note: All numbers or variables have
1
an exponent of ONE. So, x is the same as x and 3 is
1
the same as 3 and so on.
Placement of the Negative
• Placement of the negative is
important!
• For example, when simplifying
an expression you have to
follow the order of operations
•  2 2 means square 2 and then
mult. by -1.
• But(2) 2means multiply
• -2 by-2
 2  4
2
(2)  4
2
Your Turn
4
2
= -16
(-1)4 = 1
32
0
=1
 3x
(4)
0
2
= -3
= 16
-14 = -1
 17
0
= -1
• When multiplying numbers or variables
with like bases ADD the exponents.
x x  x
a
b
( a b )
Think about it. Say you’re multiplying x3·x2. X3 means x·x·x and x2
means x·x. So x·x·x·x·x = x5. Add the exponents to get the correct
power.
x x  x
3
5
( 3 5 )
x
8
x x x
4
3
x
9
2
Example 3
You Try It!
8 8
7
4
8
3
Example 4
NOTE: Multiply the coefficients and add the
exponents on the like bases. Leave the
bases the same.
6 x  3x  6  3  x
3
5
( 3 5 )
 18 x
8
Example 5
7 x  3x
5
6
11
21x
Example 6
5 x  3x
15x
2
Example 7
3x y 10 x y
5
2
7
7
30 x y
8
Power of a Power
• To Find the Power of a Power, Multiply the
EXPONENTS.
– For Instance:
m
n
(a )
=
m*n
a
Be sure to multiply the exponent outside the parentheses by all of the
exponents inside the parentheses!
Example 1
3
4
(x )
12
=x
Example 2
2
3
(x )
6
x
Example 3
4 3
(xy )
3 12
x y
Example 4
3 2
(5m )
2
6
5m
or
6
25m
Example 5
4 3
(2 y )
Answer
3
2 y
12
or
8y
12
• We can divide two quantities with
exponents if they have the same base. To
divide two quantities with the same base,
subtract the exponents and keep the base
the same.
a
•
x
( a b )

x
b
x
Example 1
5
x
( 5 3)
2

x

x
3
x
Example 2
You Try It!
10
x
3
x
x
7
Example 3
You Try It!
8
2
3
2
2
5
or
32
Example 4
• NOTE: Simplify the fraction part and
subtract the exponents.
4
4x
2
12 x
1 2
x
3
2
or
x
3
Example 5
• NOTE: Simplify the fraction part and
subtract the exponents.
6
24 x
3
6x
4x
3
• Let’s define a number with a negative
exponent to be the reciprocal of that
power with a positive exponent. So, to
simplify an expression with a negative
exponent, take the reciprocal, and make
the exponent positive.
–For Instance:
x
a
1
 a
x
• In other words, move the factor with the
negative exponent to the other side of the
fraction bar and make the exponent
positive.
• So, if a factor with a negative exponent is
in the numerator, move it to the
denominator and make the exponent
positive, and vice versa.
Example 1
x
3
1
3
x
Example 2
2
3
1
3
2
or
1
8
Example 3
3
x y
2
Hint: the negative exponent only applies to the number or
variable it is directly beside
2
y
3
x
Example 4
6
2
5
 6  5  6 25
2
 150
The exponent indicates the number of
times the _____ is used as a _______.
__________
_________
= _______________
Zero Exponents
Any number raised to the zero power
equals one!
Ex)
10
0
Ex)
= __
0 = __
1
Ex)
0
729 = __
Another important note: All numbers or variables have
1
an exponent of ONE. So, x is the same as x and 3 is
1
the same as 3 and so on.
Placement of the Negative
• Placement of the negative is
important!
• For example, when simplifying
an expression you have to
follow the order of operations
•
means square 2 and then
mult. by -1.
 22
• But
-2
means multiply -2 by
(2)
2
 2  ____
2
(2)  ____
2
Your Turn
4
2
(-1)4
32
0
 3x
(4)
0
2
-14
 17
0
• When multiplying numbers or variables
with like bases _____ the exponents.
x x  x
a
b
( a b )
Think about it. Say you’re multiplying x3·x2. X3 means x·x·x and x2
means x·x. So x·x·x·x·x = x5. Add the exponents to get the correct
power.
x x  x
3
5
( 3 5 )
x
__
x x x
4
3
2
Example 3
You Try It!
Remember to keep the base
the same.
8 8
4
3
Example 4
• NOTE: Multiply the coefficients and add
the exponents on the like bases. Leave
the base the same.
6 x  3x 
3
5
6 3 x
__ x
__
( 3 5 )

Example 5
You Try It!
7 x  3x
5
6
Example 6
5 x  3x
Example 7
3x y 10 x y
5
2
7
Power of a Power
• To Find the Power of a Power, ________
the EXPONENTS.
– For Instance:
m
n
(a )
=
m*n
a
Be sure to multiply the exponent outside the parentheses by all of the
exponents inside the parentheses!
Example 1
3
4
(x )
Example 2
2
3
(x )
Example 3
4 3
(xy )
Example 4
3 2
(5m )
Example 5
4 3
(2 y )
• We can divide two quantities with
exponents if they have the same base. To
divide two quantities with the same base,
________________________ and
______________.
a
•
x
( a b )

x
b
x
Example 1
5
x
( 5 3)
__

x

x
3
x
Example 2
You Try It!
10
x
3
x
Example 3
You Try It!
8
2
3
2
Example 4
• NOTE: Simplify the fraction part and
subtract the exponents.
4
4x
2
12 x
Example 5
• NOTE: Simplify the fraction part and
subtract the exponents.
6
24 x
3
6x
• Let’s define a number with a negative
exponent to be the reciprocal of that
power with a positive exponent. So, to
simplify an expression with a negative
exponent, take the reciprocal, and make
the exponent positive.
–For Instance:
x
a
1
 a
x
• In other words, move the factor with the
negative exponent to the other side of the
fraction bar and make the exponent
positive.
• So, if a factor with a negative exponent is
in the numerator, move it to the
denominator and make the exponent
positive, and vice versa.
Example 1
x
3
Example 2
2
3
Example 3
3
x y
2
Hint: the negative exponent only applies to the number or
variable it is directly beside
Example 4
6
2
5