Simplify. Express your answer using exponents. \( \left(g^{12} h^{-2}\right)^{-2} \)

To simplify \( \left(g^{12} h^{-2}\right)^{-2} \), we apply the power of a power rule, which states that \( (a^m)^n = a^{m \cdot n} \). So we distribute the exponent \(-2\) to both terms inside the parentheses: \[ \left(g^{12}\right)^{-2} \cdot \left(h^{-2}\right)^{-2} = g^{12 \cdot (-2)} \cdot h^{-2 \cdot (-2)} = g^{-24} \cdot h^{4} \] Now, we can express this using positive exponents by rewriting \(g^{-24}\) as \(\frac{1}{g^{24}}\): \[ \frac{h^4}{g^{24}} \] Thus, the final simplified expression is: \[ \frac{h^4}{g^{24}} \]