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.

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.

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.

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

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

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

** multiplication of like variables affects their exponents.

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

** multiplication of like variables affects their exponents.

The algebraic rule is :

MONOMIAL MULTIPLICATION & DIVISION𝑥𝑚 ∙ 𝑥𝑛=𝑥𝑚+𝑛

EXAMPLE # 1 :

MONOMIAL MULTIPLICATION & DIVISION𝑥𝑚 ∙ 𝑥𝑛=𝑥𝑚+𝑛

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

MONOMIAL MULTIPLICATION & DIVISION𝑥𝑚 ∙ 𝑥𝑛=𝑥𝑚+𝑛

EXAMPLE # 1 :

EXAMPLE # 2 :

1

MONOMIAL MULTIPLICATION & DIVISION𝑥𝑚 ∙ 𝑥𝑛=𝑥𝑚+𝑛

EXAMPLE # 1 :

EXAMPLE # 2 :

EXAMPLE # 3 :

1

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

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

Dividing LIKE variables also affects their exponents…

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

If I had to simplify , I could use the principle

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

If I had to simplify , I could use the principle

Since we can say anything divided by itself = 1

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

If I had to simplify , I could use the principle

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

Since we can say anything divided by itself = 1

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

If I had to simplify , I could use the principle

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

This leaves

Since we can say anything divided by itself = 1

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

If I had to simplify , I could use the principle

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

This leaves

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

Since we can say anything divided by itself = 1

MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )

MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )

EXAMPLE # 4 :

MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )

EXAMPLE # 4 :

EXAMPLE # 5 :

MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )

EXAMPLE # 4 :

EXAMPLE # 5 :

EXAMPLE # 6 :

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE : Simplify

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE : Simplify

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

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE : Simplify

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

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

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE : Simplify

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

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

Multiply any #’s and apply the proper RULE…

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE : Simplify

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

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

Multiply any #’s and apply the proper RULE…

Write your answer…

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 7 : Simplify

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 7 : Simplify

Rewrite …

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 7 : Simplify

Rewrite … multiply any #’s and apply rule …

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 7 : Simplify

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

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 8 : Simplify

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 8 : Simplify

Rewrite …

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 8 : Simplify

Rewrite … divide any #’s and apply rule …

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 8 : Simplify

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

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 9 : Simplify

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 9 : Simplify

Rewrite …

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 9 : Simplify

Rewrite … simplify fraction and apply rule …

MONOMIAL MULTIPLICATION & DIVISIONRULES : OR

EXAMPLE # 9 : Simplify

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.

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 :

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 :

EXAMPLE :

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 :

EXAMPLE :

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