How do you simplify $(x^3y^2)^(3/2)/(x^-1y^(-2/3))^(1/4)$ ?

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Answer 1 · 2017-11-01T10:55:19

$color(magenta)(x^(19/4)y^(19/6)$

$((x^3y^2)^(3/2))/(x^-1y^(-2/3))^(1/4)$

$:.=(x^(9/2)y^(6/2))/(x^(-1/4)y^(-2/12))$

$:.=(x^(9/2)y^3)/(x^(-1/4)y^(-2/12))$

$:.=(x^(9/2)y^3)/(x^(-1/4)y^(-1/6))$

$:.=x^(9/2+1/4)y^(3+1/6)$

$:.=x^(9/2+1/4)y^(19/6)$

$:.=x^((18+1)/4)y^(19/6)$

$:.color(magenta)(=x^(19/4)y^(19/6)$

How do you simplify (x^3y^2)^(3/2)/(x^-1y^(-2/3))^(1/4)(x^3y^2)^(3/2)/(x^-1y^(-2/3))^(1/4)?