What is the solution of the equation (3/5)^6(x+1)-(27/125)^(x-3)=0?

For the given expression to become an equation, you'll
have to write:

(3/5)^6(x+1)-(27/125)^(x-3) =
0

We notice that 27/125 =
(3/5)^3

Writing 27/125 as (3/5)^3, we'll create matching
bases.

The equation will
become:

(3/5)^6(x+1)-(3/5)^3(x-3) =
0

We'll shift (3/5)^3(x-3) to the
right:

(3/5)^6(x+1) =
(3/5)^3(x-3)

Since the bases are matching, we'll apply one
to one rule of exponentials:

6(x+1) =
3(x-3)

We'll divide by
3:

2(x+1) = x - 3

We'll remove
the brackets:

2x + 2 = x -
3

We'll isolate x to the left
side:

2x - x = -2 - 3

x =
-5

The solution of the equation is x =
-5.