Question

Simplify and write without negative exponents

Answer 1

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