monomial multiplication & division we added and subtracted monomials in the last section. it is...

MONOMIAL MULTIPLICATION & DIVISIONWe added and subtracted monomials in the last section. It is time to multiply and divide monomials.


But before we do that, we need to cover the rules for multiplication and division of like variables.



RULE : when multiplying like variables, you ADD their exponents.




EXAMPLE : If I had , we can see there are five ’s





SO NOT





SO NOT

** multiplication of like variables affects their exponents.





SO NOT

** multiplication of like variables affects their exponents.

The algebraic rule is :

MONOMIAL MULTIPLICATION & DIVISION𝑥𝑚 ∙ 𝑥𝑛=𝑥𝑚+𝑛

EXAMPLE # 1 :


EXAMPLE # 1 : NOTE : variables that have no exponents listed have an assumed 1 to be their exponent. It is not necessary to write the 1. However, if it helps you remember it is there, go ahead and write it.

1


EXAMPLE # 1 :

EXAMPLE # 2 :

1


EXAMPLE # 1 :

EXAMPLE # 2 :

EXAMPLE # 3 :

1

MONOMIAL MULTIPLICATION & DIVISIONRULE : when dividing like variables, you subtract their exponents.


Dividing LIKE variables also affects their exponents…


If I had to simplify , I could use the principle



Since we can say anything divided by itself = 1



So to simplify I could begin to reduce as many pairs as I can





This leaves





This leaves

The term “cancel” is often used to describe this… so the pairs “cancel out”


MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )


EXAMPLE # 4 :


EXAMPLE # 4 :

EXAMPLE # 5 :


EXAMPLE # 4 :

EXAMPLE # 5 :

EXAMPLE # 6 :

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE : Simplify


EXAMPLE : Simplify

Breaking down the problem into smaller “mini” problems helps when simplifying…


EXAMPLE : Simplify


Rewrite the problem with all coefficients together and all like variables…


EXAMPLE : Simplify



Multiply any #’s and apply the proper RULE…


EXAMPLE : Simplify



Multiply any #’s and apply the proper RULE…

Write your answer…


EXAMPLE # 7 : Simplify



Rewrite …



Rewrite … multiply any #’s and apply rule …



Rewrite … multiply any #’s and apply rule … get your final answer



Rewrite …



Rewrite … divide any #’s and apply rule …



Rewrite … divide any #’s and apply rule … get your answer



Rewrite …



Rewrite … simplify fraction and apply rule …



Rewrite … simplify fraction and apply rule … get your answer

MONOMIAL MULTIPLICATION & DIVISIONNOTE : When dividing LIKE variables and subtracting exponents, it is possible to get a zero as the result of the exponent subtraction. When that happens, there is a rule that anything to the zero power = 1.


EXAMPLES :


EXAMPLES :

EXAMPLE :


EXAMPLES :

EXAMPLE :

That is why the “cancelling” works, anything divided by itself = 1 ( mind blown ? )

monomial multiplication & division we added and subtracted monomials in the last section. it is...

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