di) \( \frac{16-4^{x}}{2^{x}-4} \)

The expression \( \frac{16-4^{x}}{2^{x}-4} \) can be simplified by recognizing that \( 4^x = (2^2)^x = 2^{2x} \). Thus, the expression becomes \( \frac{16 - 2^{2x}}{2^x - 4} \). You can further simplify the numerator \( 16 - 2^{2x} \) to \( 4 - (2^x)^2 \), which is a difference of squares, hence it can be factored as \( (4 - 2^x)(4 + 2^x) \). Now, rewriting the original expression, we have: \[ \frac{(4 - 2^x)(4 + 2^x)}{2^x - 4} \] Notice that \( 2^x - 4 \) is equivalent to \( -(4 - 2^x) \). Thus, the expression simplifies into: \[ -(4 + 2^x) \] So, the final simplified result of the expression is \( -(4 + 2^x) \).