To calculate the missing value of "x" in the expression (11/9)^3 × (9/11)^6 = (11/9)^(2x-1), we can compare the exponents on both sides of the equation.
On the left side, we have (11/9)^3 × (9/11)^6. This can be simplified by using the properties of exponents and canceling out common factors:
(11/9)^3 × (9/11)^6 = (11/9)^(3+6).
Now, let's compare this to the right side of the equation, which is (11/9)^(2x-1).
We can set the exponents equal to each other:
3 + 6 = 2x - 1.
Simplifying the left side, we have:
9 = 2x - 1.
Next, we can isolate the variable by adding 1 to both sides of the equation:
9 + 1 = 2x - 1 + 1.
This gives us:
10 = 2x.
Finally, we can solve for x by dividing both sides of the equation by 2:
10/2 = 2x/2.
This simplifies to:
5 = x.
Therefore, the missing value of "x" in the expression (11/9)^3 × (9/11)^6 = (11/9)^(2x-1) is x = 5.