The given expression is:
[tex] \sqrt[5]{64 x^{7} w^{5} } [/tex]
The expression can be simplified as follows:
[tex]\sqrt[5]{64 x^{7} w^{5} } \\ \\
= \sqrt[5]{(2)^{6} x^{7} w^{5} } \\ \\
= \sqrt[5]{(2)^{5}*2* x^{5}* x^{2} * w^{5} } \\ \\
= \sqrt[5]{ (2^{5} x^{5} w^{5} )*2 x^{2} } \\ \\
= \sqrt[5]{(2xw)^{5}*2 x^{2} } \\ \\
=2xw* \sqrt[5]{2x^{2} }
[/tex]
