Answer:
[tex]xy^5\sqrt[3]{xy}[/tex]
Step-by-step explanation:
Use properties
[tex](ab)^n=a^nb^n\\ \\(a^n)^m=a^{nm}\\ \\a^{m+n}=a^m\cdot a^n[/tex]
Then
[tex](x^2y^8)^{\frac{2}{3}}=(x^2)^{\frac{2}{3}}\cdot (y^8)^{\frac{2}{3}}=x^{2\cdot \frac{2}{3}}\cdot y^{8\cdot \frac{2}{3}}=x^{\frac{4}{3}}\cdot y^{\frac{16}{3}}[/tex]
Note that
[tex]x^{\frac{4}{3}}=x^{1+\frac{1}{3}}=x^1\cdot x^{\frac{1}{3}}=x\sqrt[3]{x}\\ \\ y^{\frac{16}{3}}=y^{5+\frac{1}{3}}=y^5\cdot y^{\frac{1}{3}}=y^5\sqrt[3]{y},[/tex]
then
[tex](x^2y^8)^{\frac{2}{3}}=x\sqrt[3]{x} \cdot y^5\sqrt[3]{y}=xy^5\sqrt[3]{xy}[/tex]
