WHEN MULTIPLYING LIKE BASES,
YOU ADD THE EXPONENTS
  
 a n  m
FOR EXAMPLE:
 3 2  5
4 4
NOW YOU TRY:
 4 6  4 
 3 7
4 1 0

WHEN RAISING A POWER TO A
POWER, YOU MULTIPLY THE
EXPONENTS
  m
 a nm
 
FOR EXAMPLE:
6
 3 4 * 6  3 24
NOW YOU TRY:
 
5
 4 3 * 5  4 15

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:
 1 2
5

5
2
NOW YOU TRY:
9
15
 1

15
9

WHEN DIVIDING LIKE BASES, YOU
SUBTRACT THE EXPONENTS.

 a a n m


 a n  m

 x x
5
3
FOR EXAMPLE:


 x 5  3  x 2
NOW YOU TRY:

 x x
12
4


 x 12  4  x 8

ANY NUMBER RAISED TO THE FIRST
POWER IS ITSELF.
a 1  a
FOR EXAMPLE:
3 1  3
NOW YOU TRY:
528921 1  528921

ANY NUMBER RAISED TO THE ZERO
POWER IS ONE.
a 0  1
FOR EXAMPLE:
3 0  1
NOW YOU TRY:
528921 0  1

HOW DO WE GET ANY NUMBER
RAISED TO THE ZERO POWER
EQUAL TO ONE?
a 0  1 a 0
Can be written as a 1  1
Working backward-you subtract the exponents when you are dividing like bases
.
1 a 1  1  a a 1
Then any number divided by itself will give you
ONE!!!

TRY THESE ON YOUR OWN:

 x x
5
3


 1


 x x
5
3


 4
 x x
1
2
1
8

TRY THESE ON YOUR OWN: x y
 3
4
 x
1
3 y 4 x y
3
 4
 x 3 y 4

TRY THIS LAST ONE ON YOUR
OWN: a a
3 b
 5 b
 2
7
 a b
8
9