The Laws of Exponents
Exponential Form:
base
exponent
Laws of Exponents:1.Multiplying
2.Dividing
3.Power to a Power
4.Zero Power
5.Negative Exponents
1. Multiplying Exponents
32 × 33 =(43)(44) = 65 · 6 =
Now try these:
(85)(32) =
23 × 32 =
Multiplying ExponentsWhat “law” or rule can you come up with for what happens when we multiply exponents?
Multiplying Exponents Law: If you are multiplying
exponents with the same base, KEEP the BASE & ADD the EXPONENTS!
m n m nx x x
512
2222 93636
So, I get it! When you multiply Powers, you add the exponents!
2. Dividing Exponents(Quotient of Powers Law)
46
43=
89
82=
35 ÷ 34 =
Now try these:56
33=
106
23=
Dividing ExponentsWhat “law” or rule can you come up with for what happens when we divide exponents?
2. Dividing Exponents Law: When dividing exponents with
the same base, KEEP the BASE & SUBTRACT the EXPONENTS!
mm n m n
n
xx x x
x
16
222
2 426
2
6
So, I get it! When you divide Powers, you subtract the exponents!
Now let’s take a look at Brain Pop and then take the quiz to see if you’re
understanding multiplying and
dividing exponents!
3. Raising a Power to a Power
(23)3 =
(54)2 =
(162)3
Power to a PowerWhat “law” or rule can you come up with for what happens when we raise a power to a power?
3. Power to a Power: If you are raising a Power to a power, you
multiply the exponents!
n
m mnx x
52323 55)5(
So, when I take a Power to a power, I multiply the exponents
4. Zero Power46
46=
89
89=
35 ÷ 35 =
4. Zero Law of Exponents: Any base powered by zero
exponent equals one.
0 1x
1)5(
1
15
0
0
0
a
and
a
and
So zero factors of a base equals 1. That makes sense! Every power has a coefficient of 1.
Negative Exponents:
http://www.virtualnerd.com/pre-algebra/factors-fractions-exponents/exponent-properties/negative-zero-exponents/negative-exponent-definition
5. Negative Exponents: If the base is powered
by the negative exponent, then the base becomes reciprocal with thepositive exponent.
1m
mx
x
933
1
125
1
5
15
2
2
3
3
and
So, when I have a Negative Exponent, I switch the base to its reciprocal with a Positive Exponent. Ha Ha!If the base with the negative exponent is in the denominator, it moves to the numerator to lose its negative sign!