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Laws of Exponents Project
9
Laws of Exponents Project
By Luis Castro
What exactly IS an exponent?
An exponent is a term that is used in math that explains how many times a number is muliplied by its self
Multiplication
It depends if its they have the same bases, or if they have different bases
If it has the same bases....
You add the exponents together.
As you can see, the exponents (x and x ) were added together to make x
If it has different bases....
You can combine the bases.
4 * 5
This changes to..
(4)(4)(4)(5)(5)(5)
Exponent to Exponent
With power to power, your just trying to raise a power to another power.
(4 )
This changes to
4
Division
This could also be broken down like this ..
4
_____
4 4
4
When dividing with exponents of different bases, it can't be simplified because the bases are unequal.
Negative Exponent
With a negative exponent, you can usually divide.
Negative exponents can be calculated one of two ways
can be solved like this..
multiplication
problem would look something like this..
Zero Power
Therefore, anything to the power of 0, is 1.
x is unequal to 0
Anything divided by itself is 0. Anything multiplied by 0 is 0.
0
Which implies that x = 1
IF
Power
to
Power
4
x (x)(x)(x) * x (x)(x)(x)(x)
3
Example of how a power to power problem may look like is
There are two ways to multiply powers
6
3 2
4
7
4
(x ) * (x ) = (x)(x)(x)(x)(x)(x)(x) = (x )
3
(cc) photo by jimmyharris on Flickr
4
3
7
3
3 2
3*2
4
6
4
2
=
4
6 2
=
6-2
There is more than one law of exponents.
When dividing with exponents of the same base, you subtract the exponents
For example
6 2
4 ÷ 4
This results to the answer..
Exponent to Exponent
(Power to power)
Multiplication
Division
Zero Power
Negative Exponents
Division
(x2)4 = (x2)(x2)(x2)(x2)
= (xx)(xx)(xx)(xx)
= xxxxxxxx
= x8
26 / 23 = 26-3 = 23 = 2·2·2 = 8