Answer:
Option d) [tex]xy^5\sqrt[3]{xy}[/tex] is correct
The simplest radical form of the given expression is [tex]xy^5.\sqrt[3]{xy}[/tex]
Step-by-step explanation:
Given expression is [tex](x^2y^8)^{\frac{2}{3}}[/tex]
To find the simplest radical form of the given expression:
[tex](x^2y^8)^{\frac{2}{3}}=((x^2y^8)^2)^{\frac{1}{3}}[/tex]
[tex]=((x^4)(y^{16}))^{\frac{1}{3}}[/tex]
[tex]=((x^4))^{\frac{1}{3}}\times (y^{16})^{\frac{1}{3}}[/tex]
[tex]=((x^3.x^1))^{\frac{1}{3}}\times (y^{15}.y^1)^{\frac{1}{3}}[/tex]
[tex]=((x^3)^{\frac{1}{3}}\times (x^1)^{\frac{1}{3}}\times (y^{15})^{\frac{1}{3}}\times (y^1)^{\frac{1}{3}}[/tex]
[tex]=x\times \sqrt[3]{x}\times y^5\times \sqrt[3]{y}[/tex]
[tex]=xy^5.\sqrt[3]{xy}[/tex]
Therefore [tex](x^2y^8)^{\frac{2}{3}}=xy^5.\sqrt[3]{xy}[/tex]
The simplest radical form is [tex]xy^5.\sqrt[3]{xy}[/tex]
Therefore Option d) [tex]xy^5\sqrt[3]{xy}[/tex] is correct
