Question

simplify. (sqrt3{27x^{6}y^{3}}) assume all variables are nonnegative. enter your answer in the box.

Explanation:

Step1: Rewrite 27 as a cube

Since \(27 = 3^3\), the expression \(\sqrt[3]{27x^{6}y^{3}}\) can be written as \(\sqrt[3]{3^{3}x^{6}y^{3}}\).

Step2: Apply cube - root property

According to the property \(\sqrt[3]{abc}=\sqrt[3]{a}\cdot\sqrt[3]{b}\cdot\sqrt[3]{c}\), we have \(\sqrt[3]{3^{3}x^{6}y^{3}}=\sqrt[3]{3^{3}}\cdot\sqrt[3]{x^{6}}\cdot\sqrt[3]{y^{3}}\).

Step3: Simplify each cube - root

We know that \(\sqrt[3]{3^{3}} = 3\), \(\sqrt[3]{x^{6}}=x^{2}\) (because \((x^{2})^{3}=x^{6}\)), and \(\sqrt[3]{y^{3}} = y\). So \(\sqrt[3]{3^{3}}\cdot\sqrt[3]{x^{6}}\cdot\sqrt[3]{y^{3}}=3x^{2}y\).

Answer:

\(3x^{2}y\)