Question

What is the expression equivalent to? Screenshots attached. Please help, ASAP! Important.

Answer 1

Choice C is the correct solution

Explanation:

We can split up the terms under the cube root sign to obtain;

`\sqrt[3]{32}*\sqrt[3]{x^(8) }*\sqrt[3]{y^(10) }\\\\\sqrt[3]{32}=\sqrt[3]{8*4}=\sqrt[3]{8}*\sqrt[3]{4}=2\sqrt[3]{4}\\\\\sqrt[3]{x^(8) }=\sqrt[3]{x^(6)*x^(2)}=\sqrt[3]{x^(6) }*\sqrt[3]{x^(2) }=x^(2)*\sqrt[3]{x^(2) }\\\\\sqrt[3]{y^(10) }=\sqrt[3]{y^(9)*y }=\sqrt[3]{y^(9) }*\sqrt[3]{y}=y^(3)*\sqrt[3]{y}`

The final step is to combine these terms;

`2\sqrt[3]{4}*x^(2)*\sqrt[3]{x^(2) }*y^(3)*\sqrt[3]{y}\\\\2x^(2)y^(3)\sqrt[3]{4x^(2)y }`