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 =415
ANY INTEGER RAISED TO NEGATIVE ONE IS THE RECIPROCAL OF THAT INTEGER. a
− 1
=
1
a
FOR EXAMPLE: 1 − 1 3 = 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: −1
9 15
15 = 9
WHEN DIVIDING LIKE BASES, YOU SUBTRACT THE EXPONENTS. a n a m
n −m = a
FOR EXAMPLE:
x x
5 3
=x
5− 3
=x
2
NOW YOU TRY:
x 12 x 4
=
x
12 −4
=x
8
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: −1
1 = 2 x
−4
1 = 8 x
x 3 x 5
x 3 x 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