Question

How to solve: \frac{1}{y^{\frac{2}{5}}} ?

Answer 1

well, there's nothing to solve per se, however assuming you meant "rationalizing the denominator", which means namely to "get rid of that pesky radical at the bottom", then


`\bf a^{( n)/( m)} \implies \sqrt[ m]{a^ n} \qquad \qquad \sqrt[ m]{a^ n}\implies a^{( n)/( m)}\\\\ -------------------------------`


`\bf \cfrac{1}{y^{(2)/(5)}}\implies \cfrac{1}{\sqrt[5]{y^2}} \quad \stackrel{rationalizing~it}{\implies }\quad \cfrac{1}{\sqrt[5]{y^2}}\cdot \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^3}}\implies \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^2}\cdot \sqrt[5]{y^3}} \\\\\\ \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^2y^3}}\implies \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^(2+3)}}\implies \cfrac{\sqrt[5]{y^3}}{\sqrt[5]{y^5}}\implies \cfrac{\sqrt[5]{y^3}}{y}`