SOLUTION: How do I simplify {{{(-2a^2*b^3)^2 /(2a^2*b)^3 }}}

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Question 187053: How do I simplify %28-2a%5E2%2Ab%5E3%29%5E2+%2F%282a%5E2%2Ab%29%5E3+
Found 2 solutions by stanbon, jim_thompson5910:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
simplify (-2a^2*b^3)^2 /(2a^2*b)^3
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= (4a^4b^6) / (8a^6b^3)
= (1/2)(b^3/a^2)
====================
Cheers,
Stan H.

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%28-2%29%5E1a%5E2%2Ab%5E3%29%5E2+%2F%28%282%29%5E1a%5E2%2Ab%5E1%29%5E3+ Rewrite -2 as %28-2%29%5E1. Rewrite 2 as %282%29%5E1. Rewrite b as b%5E1


Multiply the outer exponent by EVERY exponent in the parenthesis


%28%28-2%29%5E2a%5E4%2Ab%5E6%29+%2F%28%282%29%5E3a%5E6%2Ab%5E3%29+ Multiply


%284a%5E4%2Ab%5E6%29+%2F%288a%5E6%2Ab%5E3%29+ Square -2 to get 4. Cube 2 to get 8


%28a%5E4%2Ab%5E6%29+%2F%282a%5E6%2Ab%5E3%29+ Reduce 4%2F8 to get 1%2F2 (these are the coefficients).


%28a%5E%284-6%29%2Ab%5E%286-3%29%29+%2F%282%29+ Subtract the exponents to divide the monomials.


%28a%5E%28-2%29%2Ab%5E3%29+%2F%282%29+ Subtract


%28b%5E3%29+%2F%282a%5E2%29+ Flip the variable that has the negative exponent to make the exponent positive.


So %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