Question

What does (-54x^6/y^4)^2/3 equal to?

Answer 1

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


`\bf \left( \cfrac{-54x^6}{y^4} \right)^{(2)/(3)}\impliedby \textit{and now let's distribute the exponent} \\\\\\ \left( \cfrac{(-54)^{(2)/(3)}x^{6\cdot (2)/(3)}}{y^{4\cdot (2)/(3)}} \right)\implies \cfrac{(-54)^{(2)/(3)}x^4}{y^{(8)/(3)}}\implies \cfrac{\sqrt[3]{(-54)^2}~x^4}{\sqrt[3]{y^8}}\implies \cfrac{\sqrt[3]{2916}~x^4}{\sqrt[3]{y^6y^2}} \\\\\\ \cfrac{\sqrt[3]{4\cdot 9^3}~x^4}{\sqrt[3]{(y^2)^3y^2}}\implies \cfrac{9\sqrt[3]{4}~x^4}{y^2\sqrt[3]{y^2}}`