[tex]\bf \left( \cfrac{3x^{\frac{3}{2}}y^3}{x^2y^{-\frac{1}{2}}} \right)^{-2}\implies \left( \cfrac{3y^3y^{\frac{1}{2}}}{x^2x^{-\frac{3}{2}}} \right)^{-2}\implies
\left( \cfrac{3y^{3+\frac{1}{2}}}{x^{2-\frac{3}{2}}} \right)^{-2}\implies \left( \cfrac{3y^{\frac{7}{2}}}{x^{\frac{1}{2}}} \right)^{-2}
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\left( \cfrac{x^{\frac{1}{2}}}{3y^{\frac{7}{2}}} \right)^{+2}\implies \cfrac{x^{\frac{1}{2}\cdot 2}}{3^2y^{\frac{7}{2}\cdot 2}}\implies \cfrac{x^1}{9y^7}\implies \cfrac{x}{9y^7}[/tex]
