3.3. \( \frac{2^{x}+15.2^{x}}{2^{x+2}} \)

To simplify the expression \( \frac{2^{x}+15.2^{x}}{2^{x+2}} \), start by factoring out \( 2^{x} \) from the numerator: \[ \frac{2^{x} (1 + 15)}{2^{x+2}} = \frac{2^{x} \cdot 16}{2^{x+2}} \] Now, notice that \( 2^{x+2} = 2^{x} \cdot 2^{2} = 2^{x} \cdot 4 \). This allows you to simplify further: \[ \frac{16 \cdot 2^{x}}{2^{x} \cdot 4} = \frac{16}{4} = 4 \] So, the simplified expression is \( 4 \).