Question 169594
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{{{((a^3*b^(-2))^(-2)a^2b/(a^(-1)b))^(-2)}}}

Put 1 exponents so everything will show an exponent:

{{{((a^3*b^(-2))^(-2)a^2b^1/(a^(-1)b^1))^(-2)}}}


First do this part: {{{(a^3*b^(-2))^(-2)}}}
{{{(a^3*b^(-2))^(-2)= a^(3*(-2))*b^((-2)(-2))=a^(-6)b^4}}},
Then replace {{{(a^3*b^(-2))^(-2)}}} by {{{a^(-6)b^4}}} 

{{{(a^(-6)b^4a^2b^1/(a^(-1)b^1))^(-2)}}}

Inside the parentheses add exponents of a and of b:

{{{((a^(-4)b^5)/(a^(-1)b^1))^(-2)}}}

Now we're ready to remove the parentheses by multiplying
every inner exponent top and bottom by the outer
exponent {{{-2}}}:

{{{(a^((-4)(-2))b^(5(-2)))/(a^((-1)(-2))b^(1(-2)))}}}

{{{(a^8b^(-10))/(a^2b^(-2))}}}

Move {{{b^(-10)}}} from numerator to denominator and
change the sign of the exponent, and write {{{b^10}}}
on the bottom.
Likewise, move {{{b^(-2)}}} from denominator to numerator and
change the sign of the exponent, and write {{{b^2}}}
on the top. 

{{{(a^8b^2)/(a^2b^10)}}}

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, {{{a^(8-2)}}} or {{{a^6}}}
and place this on the top since the exponent {{{8}}} was
larger than the exponent {{{2}}} and {{{a^8}}} was on the top.
We eliminate {{{a^2}}} from the bottom:

{{{(a^6b^2)/(b^10)}}}

Finally we subtract exponents of b, {{{b^(10-2)}}} or {{{b^8}}}
and place this on the bottom since the exponent {{{10}}} was
larger than the exponent {{{2}}} and {{{b^10}}} was on the bottom.
We eliminate {{{b^2}}} from the top:

{{{(a^6)/(b^8)}}}

Edwin</pre>