Simplify the expression completely. sqrt [3](640x^3y^6) A 40xy^2 B xy^3sqrt [3](10) C 8xy^3sqrt [3](10) D 4xy^2sqrt [3](10)

To simplify the expression \(\sqrt[3]{640x^{3}y^{6}}\), we need to break it down into.<br /><br />First, let's factorize the number 640:<br />\[ 640 = 2^6 \times 5 \]<br /><br />So, the expression becomes:<br />\[ \sqrt[3]{2^6 \times 5 \times x^3 \times y^6} \]<br /><br />We can separate the cube root into individual components:<br />\[ \sqrt[3]{2^6} \times \sqrt[3]{5} \times \sqrt[3]{x^3} \times \sqrt[3]{y^6} \]<br /><br />Now, we simplify each cube root:<br />\[ \sqrt[3]{2^6} = \sqrt[3]{(2^3)^2} = 2^2 = 4 \]<br />\[ \sqrt[3]{x^3} = x \]<br />\[ \sqrt[3]{y^6} = y^2 \]<br /><br />Putting it all together, we get:<br />\[ 4 \times x \times y^2 \times \sqrt[3]{5} \]<br /><br />Thus, the simplified expression is:<br />\[ 4xy^2 \sqrt[3]{5} \]<br /><br />Therefore, the correct answer is:<br />D. \( 4xy^2 \sqrt[3]{10} \)