Why Exponents Don't Always Add Up

[Jbreezy]

Homework Statement

Why is $(-1)^{n+1} (-1)^{n+1} = (-1)^{2n+2}$ but
$(-1)^{n+1} (1)^{n+1} = (-1)^{n+1}$
I thought in both instances you are to just add the exponents.

Homework Equations

The Attempt at a Solution

 

[STEMucator]

1 to the power of anything is just 1. Right?

EDIT : Also, to be a bit more general, you need to have the same bases.

 

[Jbreezy]

Thanks. I can't even believe myself some days

 

[STEMucator]

Thanks. I can't even believe myself some days

Ha no problem :), we all have those.

 

[janhaa]

Because:
I:
$$a^x\cdot a^x=a^{x+x}$$
II:
$$a^x\cdot b^x=(a\cdot b)^{x}$$