Simplify. \[ \left(4 w^{-2} x^{4}\right)^{3} \] Write your answer using only positiv

To simplify \( \left(4 w^{-2} x^{4}\right)^{3} \), we can apply the power of a product rule. First, we raise each factor inside the parentheses to the power of 3: \[ 4^{3} = 64, \quad (w^{-2})^{3} = w^{-6}, \quad (x^{4})^{3} = x^{12}. \] Now put it all together: \[ \left(4 w^{-2} x^{4}\right)^{3} = 64 w^{-6} x^{12}. \] To express this with only positive exponents, we can rewrite \( w^{-6} \) as \( \frac{1}{w^{6}} \): \[ = \frac{64 x^{12}}{w^{6}}. \] Thus, the simplified expression is: \[ \frac{64 x^{12}}{w^{6}}. \]