Simplify. \( \left(2 w^{-2} x^{4}\right)^{-4} \) Write your answer using only positive exponents.

To simplify \( \left(2 w^{-2} x^{4}\right)^{-4} \), we start by applying the property of exponents that states \( (a^m)^n = a^{m \cdot n} \). Thus, we can distribute the exponent \(-4\) to each part inside the parentheses: \[ \left(2 w^{-2} x^{4}\right)^{-4} = 2^{-4} w^{-2 \cdot -4} x^{4 \cdot -4} \] Now simplify each term: \[ 2^{-4} = \frac{1}{2^4} = \frac{1}{16}, \quad w^{-2 \cdot -4} = w^{8}, \quad x^{4 \cdot -4} = x^{-16} \] Bringing it all together, we have: \[ \left(2 w^{-2} x^{4}\right)^{-4} = \frac{1}{16} w^{8} x^{-16} \] To express with only positive exponents, we rewrite \( x^{-16} \) as \( \frac{1}{x^{16}} \): \[ = \frac{w^{8}}{16 x^{16}} \] Thus, the simplified expression is \[ \frac{w^{8}}{16 x^{16}} \]