SOLUTION: Simplify (-2a^2 b^3)^2/(2a^2 b)^3

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Question 150543: Simplify (-2a^2 b^3)^2/(2a^2 b)^3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28-2a%5E2%2Ab%5E3%29%5E2%2F%282a%5E2%2Ab%29%5E3 Start with the given expression.


%28%28-2a%5E2%2Ab%5E3%29%28-2a%5E2%2Ab%5E3%29%29%2F%282a%5E2%2Ab%29%5E3 Expand %28-2a%5E2%2Ab%5E3%29%5E2 to get %28-2a%5E2%2Ab%5E3%29%28-2a%5E2%2Ab%5E3%29


Expand %282a%5E2%2Ab%29%5E3 to get %282a%5E2%2Ab%29%282a%5E2%2Ab%29%282a%5E2%2Ab%29


Collect and combine the three "b"s in the denominator to get b%2Ab%2Ab=b%5E3



Highlight the common terms.


Cancel out the common terms.


%28%28-1%29%28-1%29%28b%5E3%29%29%2F%282a%5E2%29 Simplify


%28b%5E3%29%2F%282a%5E2%29 Multiply


So %28-2a%5E2%2Ab%5E3%29%5E2%2F%282a%5E2%2Ab%29%5E3 simplifies to %28b%5E3%29%2F%282a%5E2%29


In other words, %28-2a%5E2%2Ab%5E3%29%5E2%2F%282a%5E2%2Ab%29%5E3=%28b%5E3%29%2F%282a%5E2%29 where a%3C%3E0 or b%3C%3E0