Express the radical in simplified form. Assume that all variables represent positive real numbers. \[ \sqrt{64 x^{3} y^{7}} \] \[ \sqrt{64 x^{3} y^{7}}=8 x^{3} y^{7} \] (Simplify your answer. Type an exact answer, using radicals as needed. Do not factor.)

Step 1 ：Given expression is \(\sqrt{64 x^{3} y^{7}}\)

Step 2 ：Take the square root of each part separately

Step 3 ：Square root of 64 is 8

Step 4 ：Square root of \(x^{3}\) is \(x^{1.5}\) or \(x\sqrt{x}\)

Step 5 ：Square root of \(y^{7}\) is \(y^{3.5}\) or \(y^{3}\sqrt{y}\)

Step 6 ：So, the simplified form of the given expression is \(8x\sqrt{x}y^{3}\sqrt{y}\)

Step 7 ：\(\boxed{8x\sqrt{x}y^{3}\sqrt{y}}\) is the final answer