# How do you simplify ((x^2y^{-3})/{x^5y^2))^{2} , giving the answer with only positive exponents?

Nov 26, 2014

${\left(\frac{{x}^{2} {y}^{- 3}}{{x}^{5} {y}^{2}}\right)}^{2}$

by dividing the numerator and denominator by ${x}^{2}$,

$= {\left(\frac{{y}^{- 3}}{{x}^{3} {y}^{2}}\right)}^{2}$

by multiplying the numerator and the denominator by ${y}^{3}$

$= {\left(\frac{1}{{x}^{3} {y}^{5}}\right)}^{2}$

by distributing the square to the numerator and the denominator,

$= \frac{{1}^{2}}{{\left({x}^{3} {y}^{5}\right)}^{2}}$

by distributing the square to each factor,

$= \frac{1}{{x}^{6} {y}^{10}}$

I hope that this was helpful.