SOLUTION: can some one explain to me in the simplest form what it means to simplify and how to simplify with an add of the following question. l am seriously looking for a tutor for l dont

Question 1108548:
can some one explain to me in the simplest form what it means to simplify and how to simplify with an add of the following question. l am seriously looking for a tutor for l dont want given answers but a teacher/ tutor to guide me.
question 1

Simplify the following expression as far as possible:
(3ab^2c^3) � (ab) � (2a^3b^4)

Found 2 solutions by math_helper, Theo:
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!

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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
(3ab^2c^3) � (ab) � (2a^3b^4)

start with (3ab^2c^3) � (ab) � (2a^3b^4)

in the rational part of the expression, you combine like terms by working on the a in the numeration and denominator, and working on the b in the numerator and the denominator.

the a in the denominator and the numerator cancels out because a/a = 1.

the b^2 in the numerator and the b in the denominator are simplified to b in the numerator because b^2 / b = b^(2-1) = b^1 = b.

you are left with (3bc^3) * (2a^3b^4)

you can remove the parentheses in this expression to get:

3bc^32a^3b^4 which is easier to see as 3 * b * c^3 * 2 * a^3 * b^4.

you would group like variables together to get (3 * 2) * (b * b^4) * c^3 * a^3

you would perform the operations indicated to get 6 * b^5 * c^3 * a^3

that can't be simplified further, so you're done.

you can then make the multiplication silent by showing it as 6b^5c^3a^3.

you have to follow the rules of PEMDAS and the rules of exponentiation and the rules of multiplication and division, and the rules of addition and subtraction.

you can also confirm your simplification is correct by assigning random values to the variables involved and evaluating the the original expression and the final expression to confirm you get the same answer.

for example:
i assigned 3 to a and 5 to b and 7 to c and got the following.

the original expression of (3ab^2c^3) � (ab) � (2a^3b^4) yielded 173643750.

the final expression of 6b^5c^3a^3 yielded 173643750.

since the answers are the same, i assume that i did the simplification correctly.

here's some references on the laws of arithmetic operations.

https://www.mathsisfun.com/operation-order-pemdas.html

https://mathlair.allfunandgames.ca/lawsofarithmetic.php

https://www.mathsisfun.com/associative-commutative-distributive.html

http://whatcom.edu/home/showdocument?id=1702

http://www.mathnstuff.com/math/spoken/here/3essay/emost.htm

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