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WHEN MULTIPLYING LIKE BASES,
YOU ADD THE EXPONENTS
a a   a
n
m
n m
FOR EXAMPLE:
3 3   3
2
5
2 5
3
7
NOW YOU TRY:
4 4   4
6
4
6 4
 4
10
WHEN RAISING A POWER TO A
POWER, YOU MULTIPLY THE
EXPONENTS
a 
n
m
a
nm
FOR EXAMPLE:
3 
4 6
3
4 *6
3
24
NOW YOU TRY:
4 
3
5
 4 3*5  41 5
ANY INTEGER RAISED TO NEGATIVE
ONE IS THE RECIPROCAL OF THAT
INTEGER.
a
1
1

a
FOR EXAMPLE:
3
1
1

3
NOW YOU TRY:
15
1
1

15
Any fraction raised to negative one is
the reciprocal of that fraction.
a 
 
b 
1
b

a
FOR EXAMPLE:
2


5
1
5

2
NOW YOU TRY:
 9 


 15 
1
15

9
WHEN DIVIDING LIKE BASES, YOU
SUBTRACT THE EXPONENTS.
 an

am


n m


a


FOR EXAMPLE:
x5

x3



  x

5 3
 x2
NOW YOU TRY:
 x 12 
12 4
8



x
x
x4 


ANY NUMBER RAISED TO THE FIRST
POWER IS ITSELF.
a a
1
FOR EXAMPLE:
3 3
1
NOW YOU TRY:
528921  528921
1
ANY NUMBER RAISED TO THE ZERO
POWER IS ONE.
a 1
0
FOR EXAMPLE:
3 1
0
NOW YOU TRY:
528921  1
0
HOW DO WE GET ANY NUMBER
RAISED TO THE ZERO POWER
EQUAL TO ONE?
0
a
0
a 1
can be written as
a
11
Working backward-you subtract the exponents
when you are dividing like bases.
a 11
a1
 1
a
Then any number divided by itself will give you
ONE!!!
TRY THESE ON YOUR OWN:
x 
 3 
x 
1
1

2
x
x 
 3 
x 
4
1

8
x
5
5
TRY THESE ON YOUR OWN:
x

4
y
3
1
3
4
x y
x
3
4

x y
4
y
3
TRY THIS LAST ONE ON YOUR
OWN:
a b
a

5 7
9
a b
b
3
2
8