Simplify. \[ 4 v^{-1} x^{5} u x^{-5} \cdot 7 u^{9} \cdot 2 v^{8} \] Use only positive exponents in your answer.

Step 1 ：The given expression is a product of several terms. To simplify it, we can use the properties of exponents. Specifically, we know that when we multiply terms with the same base, we add the exponents. Also, a negative exponent means that the base is on the denominator.

Step 2 ：So, we can start by rearranging the terms to group those with the same base together. Then, we can apply the properties of exponents to simplify the expression.

Step 3 ：The simplified expression is \(56 u^{10} v^{7}\). This is the final answer.

Step 4 ：Final Answer: \(\boxed{56 u^{10} v^{7}}\)