SOLUTION: please help on this equation. (6a^3b)(8a^4b^2) over..... 30a^3b^2 thanks.

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Question 187173: please help on this equation.

(6a^3b)(8a^4b^2) over.....

30a^3b^2

thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First, simplify %286a%5E3b%29%288a%5E4b%5E2%29+


%286a%5E3b%29%288a%5E4b%5E2%29+ Start with the given expression.


%286%2A8%29%28a%5E3%2Aa%5E4%29%28b%2Ab%5E2%29+ Rearrange the terms.


48%28a%5E3%2Aa%5E4%29%28b%2Ab%5E2%29+ Multiply 6 and 8 to get 48


48%28a%5E%283%2B4%29%29%28b%5E%281%2B2%29%29+ Add the exponents to multiply the monomials.


48a%5E7%2Ab%5E3 Add


So %286a%5E3b%29%288a%5E4b%5E2%29=48a%5E7%2Ab%5E3


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This means that


%28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29+


simplifies to


%2848a%5E7%2Ab%5E3%29%2F%2830a%5E3b%5E2%29+


Expand.


Note: 48a%5E7b%5E3=2%2A2%2A2%2A2%2A3%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Aa%2Ab%2Ab%2Ab (there are 7 a's and 3 b's) and 30a%5E3b%5E2=2%2A3%2A5%2Aa%2Aa%2Aa%2Ab%2Ab (there are 3 a's and 3 b's)


Highlight the common terms.


Cancel out the common terms.


%282%2A2%2A2%2Aa%2Aa%2Aa%2Aa%2Ab%29%2F%285%29 Simplify.


%288a%5E4b%29%2F%285%29 Regroup and multiply.


So %2848a%5E7b%5E3%29%2F%2830a%5E3b%5E2%29 simplifies to %288a%5E4b%29%2F%285%29.



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Answer:


So %28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29+


simplifies to %288a%5E4b%29%2F%285%29


In other words, %28%286a%5E3b%29%288a%5E4b%5E2%29%29%2F%2830a%5E3b%5E2%29=%288a%5E4b%29%2F%285%29