Answer:
[tex]\large\boxed{8x^3y^4\sqrt[3]{xy}}[/tex]
Step-by-step explanation:
[tex]\sqrt[3]{125x^{10}y^{13}}+\sqrt[3]{27x^{10}y^{13}}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}\\\\=\sqrt[3]{125}\cdot\sqrt[3]{x^{10}y^{13}}+\sqrt[3]{27}\cdot\sqrt[3]{x^{10}y^{13}}\\\\=5\sqrt[3]{x^{10}y^{13}}+3\sqrt[3]{x^{10}y^{13}}\\\\=8\sqrt[3]{x^{10}y^{13}}\\\\=8\sqrt[3]{x^{3+3+3+1}y^{3+3+3+3+1}}\qquad\text{use}\ a^na^m=a^{n+m}\\\\=8\sqrt[3]{x^3x^3x^3xy^3y^3y^3y}\qquad\text{use}\ \sqrt[n]{ab}=\sqrt[n]{a}\cdot\sqrt[n]{b}[/tex]
[tex]=8\sqrt[3]{x^3}\cdot\sqrt[3]{x^3}\cdot\sqrt[3]{x^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{y^3}\cdot\sqrt[3]{xy}\qquad\text{use}\ \sqrt[n]{a^n}=a\\\\=8xxxyyyy\sqrt[3]{xy}\\\\=8x^3y^4\sqrt[3]{xy}[/tex]
