Ask Me Help Desk - Rules for addition of powers when bases are the same and signs are negative?

Are you trying to solve this:

$ 1.5^{11} = (-1.5)^n + 5 $

(which is what you wrote) or this:

$ 1.5^{11} = (-1.5)^{n + 5} $

For now I will assume the latter. The right hand side can be rewritten to give you:

$ 1.5^{11} \ = \ -1^{(n+5)}\ \times \ 1.5^{(n+5)} $

You can see that the value of n+5 = 11. So what is the value for n? But note that the left hand side is a positive number while the right hand side is positive only if
-1 is raised to an even power. Does the value for n that you just found work? What does this tell you about this equation?