Question

Multiply and simplify this equation.

Answer 1

`-3\sqrt[3]{4}y^{(5)/(3)}\sqrt[3]{x^2}\sqrt[3]{x}`

Explanation:

`\sqrt[3]{-9x^2y^4} \cdot \sqrt[3]{12xy}`

`=\sqrt[3]{9}\sqrt[3]{x^2}\left(-y\sqrt[3]{y}\right)\sqrt[3]{12xy}`

`=\sqrt[3]{9}\sqrt[3]{x^2}\left(-y\sqrt[3]{y}\right)\sqrt[3]{12}\sqrt[3]{x}\sqrt[3]{y}`

`=\sqrt[3]{108}\sqrt[3]{x^2}\left(-y\sqrt[3]{y}\right)\sqrt[3]{x}\sqrt[3]{y}`

`=\sqrt[3]{4}\cdot \:3\sqrt[3]{x^2}\left(-y\sqrt[3]{y}\right)\sqrt[3]{x}\sqrt[3]{y}`

`=-\sqrt[3]{4}\cdot \:3\sqrt[3]{x^2}y\sqrt[3]{y}\sqrt[3]{x}\sqrt[3]{y}`

`=-\sqrt[3]{4}\cdot \:3\sqrt[3]{x^2}y\left(\sqrt[3]{y}\right)^2\sqrt[3]{x}`

`=-\sqrt[3]{4}\cdot \:3\sqrt[3]{x^2}y^{(5)/(3)}\sqrt[3]{x}`

`=-3\sqrt[3]{4}y^{(5)/(3)}\sqrt[3]{x^2}\sqrt[3]{x}`