Question

Write the following expression in simplified radical form. 5th root (64x to the 7th power w to the 5th power)

Answer 1

The given expression is:

$\sqrt[5]{64 x^{7} w^{5} }$

The expression can be simplified as follows:

$\sqrt[5]{64 x^{7} w^{5} } \\ \\ = \sqrt[5]{(2)^{6} x^{7} w^{5} } \\ \\ = \sqrt[5]{(2)^{5}*2* x^{5}* x^{2} * w^{5} } \\ \\ = \sqrt[5]{ (2^{5} x^{5} w^{5} )*2 x^{2} } \\ \\ = \sqrt[5]{(2xw)^{5}*2 x^{2} } \\ \\ =2xw* \sqrt[5]{2x^{2} }$