one way to see this kind of problems is knowing that:
[tex]\sqrt[3]{x}^2=x^{\frac{2}{3}}^{}[/tex]so, using sqrt properties
[tex]\sqrt[3]{27\cdot x^{15}\cdot y^{72}}=\sqrt[3]{27}\cdot\sqrt[3]{x^{15}}\cdot\sqrt[3]{y^{72}}[/tex][tex]\sqrt[3]{27}\cdot\sqrt[3]{x^{15}}\cdot\sqrt[3]{y^{72}}=3\cdot x^{\frac{15}{3}}\cdot y^{\frac{72}{3}}[/tex][tex]3\cdot x^{\frac{15}{3}}\cdot y^{\frac{72}{3}}=3\cdot x^5\cdot y^{24}[/tex]So the answer is=
[tex]3\cdot x^5\cdot y^{24}[/tex]