To solve this expression, we need to follow the order of operations (also known as PEMDAS or BODMAS).

First, we need to calculate the exponentiation.

3^9 = 19683
3^7 = 2187

Now, we can substitute these values back into the expression:

84 : 4 + 19683 : 2187

Next, we need to perform the division:

84 ÷ 4 + 19683 ÷ 2187

84 ÷ 4 = 21
19683 ÷ 2187 = 9

Now, we can simplify the expression further:

21 + 9 = 30

Therefore, the value of the expression 84 : 4 + 3^9 : 3^7 is 30.