We can break down the expression as follows:
3^√20 can be simplified as 3^2 3^√16, since 20 = 4 5 = 2^2 5. This gives us 9 2 * 3^√16.
Now, 3^√16 can be simplified further as 3^4, since 16 = 4^2. This gives us 9 2 81.
So, 3^√20 = 162.
Now, we can substitute this value in the expression:
162 + 14√2 + 162 - 14√2= 162 + 162= 324
Therefore, the simplified expression is 324.
We can break down the expression as follows:
3^√20 can be simplified as 3^2 3^√16, since 20 = 4 5 = 2^2 5. This gives us 9 2 * 3^√16.
Now, 3^√16 can be simplified further as 3^4, since 16 = 4^2. This gives us 9 2 81.
So, 3^√20 = 162.
Now, we can substitute this value in the expression:
162 + 14√2 + 162 - 14√2
= 162 + 162
= 324
Therefore, the simplified expression is 324.