MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time...
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Transcript of MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time...
![Page 1: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/1.jpg)
MONOMIAL MULTIPLICATION & DIVISIONWe added and subtracted monomials in the last section. It is time to multiply and divide monomials.
![Page 2: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/2.jpg)
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.
![Page 3: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/3.jpg)
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.
![Page 4: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/4.jpg)
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
![Page 5: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/5.jpg)
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
![Page 6: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/6.jpg)
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.
![Page 7: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/7.jpg)
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 :
![Page 8: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/8.jpg)
MONOMIAL MULTIPLICATION & DIVISION𝑥𝑚 ∙ 𝑥𝑛=𝑥𝑚+𝑛
EXAMPLE # 1 :
![Page 9: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/9.jpg)
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
![Page 10: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/10.jpg)
MONOMIAL MULTIPLICATION & DIVISION𝑥𝑚 ∙ 𝑥𝑛=𝑥𝑚+𝑛
EXAMPLE # 1 :
EXAMPLE # 2 :
1
![Page 11: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/11.jpg)
MONOMIAL MULTIPLICATION & DIVISION𝑥𝑚 ∙ 𝑥𝑛=𝑥𝑚+𝑛
EXAMPLE # 1 :
EXAMPLE # 2 :
EXAMPLE # 3 :
1
![Page 12: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/12.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULE : when dividing like variables, you subtract their exponents.
![Page 13: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/13.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULE : when dividing like variables, you subtract their exponents.
Dividing LIKE variables also affects their exponents…
![Page 14: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/14.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULE : when dividing like variables, you subtract their exponents.
If I had to simplify , I could use the principle
![Page 15: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/15.jpg)
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
![Page 16: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/16.jpg)
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
![Page 17: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/17.jpg)
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
![Page 18: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/18.jpg)
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
![Page 19: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/19.jpg)
MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )
![Page 20: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/20.jpg)
MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )
EXAMPLE # 4 :
![Page 21: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/21.jpg)
MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )
EXAMPLE # 4 :
EXAMPLE # 5 :
![Page 22: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/22.jpg)
MONOMIAL MULTIPLICATION & DIVISIONAlgebraic rule ( division of like variables )
EXAMPLE # 4 :
EXAMPLE # 5 :
EXAMPLE # 6 :
![Page 23: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/23.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE : Simplify
![Page 24: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/24.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE : Simplify
Breaking down the problem into smaller “mini” problems helps when simplifying…
![Page 25: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/25.jpg)
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…
![Page 26: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/26.jpg)
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…
![Page 27: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/27.jpg)
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…
![Page 28: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/28.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 7 : Simplify
![Page 29: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/29.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 7 : Simplify
Rewrite …
![Page 30: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/30.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 7 : Simplify
Rewrite … multiply any #’s and apply rule …
![Page 31: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/31.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 7 : Simplify
Rewrite … multiply any #’s and apply rule … get your final answer
![Page 32: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/32.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 8 : Simplify
![Page 33: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/33.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 8 : Simplify
Rewrite …
![Page 34: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/34.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 8 : Simplify
Rewrite … divide any #’s and apply rule …
![Page 35: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/35.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 8 : Simplify
Rewrite … divide any #’s and apply rule … get your answer
![Page 36: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/36.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 9 : Simplify
![Page 37: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/37.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 9 : Simplify
Rewrite …
![Page 38: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/38.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 9 : Simplify
Rewrite … simplify fraction and apply rule …
![Page 39: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/39.jpg)
MONOMIAL MULTIPLICATION & DIVISIONRULES : OR
EXAMPLE # 9 : Simplify
Rewrite … simplify fraction and apply rule … get your answer
![Page 40: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/40.jpg)
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.
![Page 41: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/41.jpg)
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 :
![Page 42: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/42.jpg)
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 :
![Page 43: MONOMIAL MULTIPLICATION & DIVISION We added and subtracted monomials in the last section. It is time to multiply and divide monomials.](https://reader036.fdocuments.in/reader036/viewer/2022062306/5a4d1ada7f8b9ab059974824/html5/thumbnails/43.jpg)
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 ? )