Answer:Option (2)Step-by-step explanation:Given expression is [tex]\sqrt[3]{64a^6b^7c^9}[/tex]By simplifying this expression,[tex]\sqrt[3]{64a^6b^7c^9}=\sqrt[3]{(4)^3(a^2)^3(b^2)^3(b)(c^3)^3}[/tex] [tex]=(4a^2b^2c^3)\sqrt[3]{b}[/tex]Option (1) [tex]2abc^2\sqrt[3]{4a^2b^3c}[/tex] = [tex]2ab^2c^2\sqrt[3]{a^2c}[/tex]Option (2)[tex]4a^2b^2c^3(\sqrt[3]{b})[/tex] [Fully simplified form]Option (3) [tex]8a^3b^3c^4(\sqrt[3]{bc} )[/tex] [Fully simplified form]Option (4)[tex]8a^2b^2c^3(\sqrt[3]{b})[/tex]Expression given in Option (2) is equivalent to the given expression.Option (2) will be the answer.