(2^n+2 + 2^n-2):2^n

To simplify the expression \((2^{n+2} + 2^{n-2}) : 2^n\), we can rewrite it as follows: \[ \frac{2^{n+2} + 2^{n-2}}{2^n} \] Now, we can split the fraction: \[ \frac{2^{n+2}}{2^n} + \frac{2^{n-2}}{2^n} \] We can simplify each term: 1. For the first term: \[ \frac{2^{n+2}}{2^n} = 2^{(n+2) - n} = 2^2 = 4 \] 2. For the second term: \[ \frac{2^{n-2}}{2^n} = 2^{(n-2) - n} = 2^{-2} = \frac{1}{4} \] Now, combining both results: \[ 4 + \frac{1}{4} \] To add these, we can express \(4\) as a fraction with a common denominator: \[ 4 = \frac{16}{4} \] Now, adding the fractions: \[ \frac{16}{4} + \frac{1}{4} = \frac{16 + 1}{4} = \frac{17}{4} \] Thus, the simplified expression is: \[ \frac{17}{4} \]