SOLUTION: Simplify with positive exponents: {{{((a^3*b^(-2))^(-2)a^2b/(a^(-1)b))^(-2)}}}

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Question 169594: Simplify with positive exponents:

Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!



Put 1 exponents so everything will show an exponent:




First do this part: 
,
Then replace  by  



Inside the parentheses add exponents of a and of b:



Now we're ready to remove the parentheses by multiplying
every inner exponent top and bottom by the outer
exponent :





Move  from numerator to denominator and
change the sign of the exponent, and write 
on the bottom.
Likewise, move  from denominator to numerator and
change the sign of the exponent, and write 
on the top. 



Subtract exponents, larger minus smaller, and place the
result in the numerator or denominator, depending on
which one had the larger exponent before.

So we subtract exponents of a,  or 
and place this on the top since the exponent  was
larger than the exponent  and  was on the top.
We eliminate  from the bottom:



Finally we subtract exponents of b,  or 
and place this on the bottom since the exponent  was
larger than the exponent  and  was on the bottom.
We eliminate  from the top:



Edwin

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