Question

((81x^3 y^(-1/3))^1/4)/(x^2 y)^1/4 simplify

Answer 1

`\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^( n)} \qquad \qquad \sqrt[{ m}]{a^( n)}\implies a^{\frac{{ n}}{{ m}}} \\\\\\ \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^( n)} \qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\`


`\bf \cfrac{\left( 81x^3y^{-(1)/(3)} \right)^{(1)/(4)}}{(x^2y)^{(1)/(4)}}\implies \cfrac{81^{(1)/(4)}x^{3\cdot {(1)/(4)}}y^{-(1)/(3)\cdot {(1)/(4)}}}{x^{2\cdot {(1)/(4)}}y^{(1)/(4)}}\implies \cfrac{81^{(1)/(4)}x^{(3)/(4)}y^{-(1)/(12)}}{x^{(2)/(4)} y^{(1)/(4)}}`


`\bf \cfrac{81^{(1)/(4)}x^{(3)/(4)}x^{-(2)/(4)}}{ y^{(1)/(4)}y^{(1)/(12)}}\implies \cfrac{(3^4)^{(1)/(4)}x^{(3)/(4)-(2)/(4)}}{y^{(1)/(4)+(1)/(12)}}\implies \cfrac{3^{4\cdot (1)/(4)}x^{(1)/(4)}}{y^{(4)/(12)}}\implies \cfrac{3^{(4)/(4)}x^{(1)/(4)}}{y^{(1)/(3)}} \\\\\\ \cfrac{3\sqrt[4]{x}}{\sqrt[3]{y}}`