Students Mentoring Students Presents: Learning Exponents!

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STUDENTS MENTORING STUDENTS
PRESENTS:
Ruben Sanchez
[email protected]
BEFORE WE START:
• We are here to help you! Do NOT be afraid
to ask questions.
• There are no dumb questions!
• The only dumb thing to do is not ask for
help when you are stuck.
LAWS OF EXPONENTS
• When dealing with exponents, there are
times we will have to operations such as
adding, subtracting, dividing, and
multiplying exponents.
• We will learn these steps by using the
methods of MADSPM (easy way to
remember it is by mad spam)
WHAT EXACTLY IS MADSPM??
•
Madspm is guide to help us understand and carry out opperations with
exponents correctly, and helps us understand what to do in math questions
involving exponents.
MA
DS
PM
WHEN WE
MULTIPLY LIKE
VARIABLE
EXPONENTS
WHEN WE DIVIDE
LIKE VARIABLE
EXPONENTS
WHEN WE HAVE
EXPONENTIAL
VARIABLES
RAISDED TO A
POWER
WE ADD THE
EXPONENTS
WE SUBTRACT
EXPONENTS
WE MULTIPLY
THE EXPONENTS
MULTIPLYING
• When we look at the MA part of MADSPM, we are dealing
with problems that involve multiplication of variables.
Lets look at an example of what to do when we multiply.
First we establish that we have 2 like variables. We continue
by multiplying the coefficients, or the numbers, in front of the
X variable.
Once we do that we come up with an answer of 21. Then we
Look at the X variable and see that both X’s are raised to the 1
Power. All we do with the X variables is add the exponent it is
Raised to. In this case both are 1, so 1+1=2. The 2 is going to be
Our new exponent of the X variable.
So what does our answer look like???
MULTIPLYING
• Lets look at another example.
We see we are going to multiply. What do we do??
1. Multiply the coefficients
2. Add the exponents of the variables
3. Get our result.
MULTIPLICATION EXERCISES
DIVIDING
• When we look at the DS part of MADSPM, we are dealing
with problems that involve division of variables.
Lets look at an example of what to do when we divide.
First we establish that we have 2 like variables. We continue
by dividing the coefficients, or the numbers, in front of the
X variable.
Once we do that we come up with an answer of 1/2. Then we
look at the X variable and see that one X variable is raised to the 4
Power and that one is raised to the 3 power. All we do with the X variables
Is subtract the exponents they are raised to. In all cases it will be the top minus
the bottom. So we are going to subtract 4-3=1
DIVIDING (CONTINUING)
Our answer will look like this. The top coefficient will be 1 and since
we are left with one X, it will stay on the top.
Note that the X will always go on the top if the exponent is positive! In this case the
exponent was a positive one, so the X is raised to the power of 1.
Lets look at what happens when we have negative exponents
DIVIDING (CONTINUING)
We carry out the same process as the previous problem. Since 2/7 is
already a simplified fraction, that stays the same. Now since we are
dividing exponents we still subtract top minus the bottom. In this case
2-5= -3.
We still write the X variable with a -3 exponent on the top but,
since we cannot have a negative exponent on the top, we need
to move it down. When we move down the negative exponent
it changes to a positive exponent.
So what would our answer look like? The fraction cannot be
simplified so it stays the same but since we bring down the
negative exponent, it turns positive when you bring it down.
 This is what our answer looks like
DIVISION EXAMPLES
POWERS RAISED TO POWERS
• When we look at the PM part of MADSPM, we are dealing
with problems that involve powers being raised to other
powers with variables.
Lets look at an example of what to do when we see powers raised to powers.
When we see this, all we do is multiply the EXPONENTS. In this case
there is no coefficient so we do not distribute to a coefficient. If there
was a number in front of X we would need to distribute a 3 to that
number as well as X.
All we do in this case is multiply 8 x 3 = 24. So what does
our answer look like? Well this is what we are supposed to get. 
POWERS RAISED TO POWERS
•
Lets look at an example when we have coefficients and a variable raised to a
power.
In this example, we are going to distribute a power of 6 to each
term inside the parenthesis. So the 2 is going to be raised to a power
of 6 and the same rule of MADSPM applies to the X variable. We only
Multiply the variable’s (letter) exponent by whatever it is being raised to.
1) So the 2 will be raised to a power of 6 to get
2) Then we multiply the X variable’s powers, 7 x 6 = 42.
Which equals
3) So our final answer looks like
POWER RAISED TO POWER EXERCISES
PRACTICE OF EVERYTHING COVERED TODAY
Multiply
Divide
Power Raised
to a Power

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