How do you simplify #(x^{\frac{1}{2}} y^{-\frac{2}{3}})(x^2 y^{\frac{1}{3}})#?

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Answer 1 · 2014-11-13T22:47:51

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

by grouping the factors with the same bases,

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

by #b^x cdot b^y=b^{x+y}#,

#=x^{1/2+2}cdot y^{-2/3+1/3}=x^{5/2}cdot y^{-1/3}#

by #b^{-x}=1/b^x#,

#=x^{5/2}/y^{1/3}={sqrt{x^5}}/{root{3}{y}}#

I hope that this was helpful.