Answer
$2^{2^7}=2^{128}=340,282, 336, 920, 938, 463, 463, 374, 607, 431, 768, 211,456$
There are $2^{2^7}$ different Boolean functions of degree $7$.
Work Step by Step
Here, we have $n=7$
The product rule states that when an event occurs in $p$ ways AND a second event occurs in $q$ ways, then the number of ways for obtaining the sequence will be as: $p \cdot q$.
Since, each Boolean variables consist of two values either 1 or 0 at one time.
Then, we have $2 . 2 ......2^7=128$ (7-tuples)
Therefore, by using product rule we have the number of Boolean functions of degree $7$ such as follows:
$2^{2^7}=2^{128}=340,282, 336, 920, 938, 463, 463, 374, 607, 431, 768, 211,456$
Thus, there are $2^{2^7}$ different Boolean functions of degree $7$.
