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

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Answer 1 · 2014-11-26T16:41:41

#({x^2y^{-3}}/{x^5y^2})^2#

by dividing the numerator and denominator by #x^2#,

#=({y^{-3}}/{x^3y^2})^2#

by multiplying the numerator and the denominator by #y^3#

#=({1}/{x^3y^5})^2#

by distributing the square to the numerator and the denominator,

#={1^2}/{(x^3y^5)^2}#

by distributing the square to each factor,

#=1/{x^6y^{10}}#

I hope that this was helpful.