Certainly! Let's break down the expression step by step:
1. Given \( n = 3 \).
2. Substitute \( n \) into the expression \( 2^{2n+1} \).
3. \( 2^{2n+1} = 2^{2*3+1} \) because \( n \) is replaced by 3.
4. Simplify the exponent: \( 2^{2*3+1} = 2^{6+1} \).
5. Perform the multiplication inside the exponent: \( 6+1 = 7 \).
6. Now we have \( 2^7 \).
7. Calculate \( 2^7 \), which equals 128.
So, when \( n = 3 \), the value of \( 2^{2n+1} \) is \( 128 \).