What is x if 11^(5x-6)=1/11^(-x-10)?

First, we'll use the negative power property of
exponentials:

1/11^(-x-10) =
11^-(-x-10)

Now, we'll re-write the
equation:

11^(5x-6) =
11^-(-x-10)

Since the bases are matching, we'll use one to
one property:

5x - 6 = x +
10

We'll isolate x to the left side. For this reason,
we'll subtract x both sides:

5x - x - 6 =
10

We'll combine like terms and we'll add 6 both
sides:

4x = 10 + 6

4x =
16

We'll divide by 4:

x =
4

The solution of the equation is x =
4.