Question

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

Answer 1

`(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}}`

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I hope that this was helpful.