#### Mos5180d

##### New member
Seems pretty basic, maybe I’m missing something.

I need to prove that (-1)^(x+1) = -(-1)^x

I can do it separately
If x is even then -1=-1
If x is odd then 1=1

But can it be done in one go?
Thanks

#### Dr.Peterson

##### Elite Member
Apply the exponent rule a^(m+n) = a^m * a^n.

#### Mos5180d

##### New member
Apply the exponent rule a^(m+n) = a^m * a^n.
Something simple as I thought! Thank you very much, this has finished off a proof I’ve been doing for quite a while

#### Jomo

##### Elite Member
If x is even then -1=-1
If x is odd then 1=1
-1 = -1 always. It does NOT depend on the parity of x.
1 = 1 always. It does NOT depend on the parity of x.

#### Dr.Peterson

##### Elite Member
I need to prove that (-1)^(x+1) = -(-1)^x

I can do it separately
If x is even then -1=-1
If x is odd then 1=1
For clarity, I think what you meant was this proof by cases:

If x is even then (-1)^(x+1) = -(-1)^x becomes -1=-1, which is true;​
If x is odd then (-1)^(x+1) = -(-1)^x becomes 1=1, which is true;​
so the statement is true in all cases.​

That is a valid method of proof, though clearly not as efficient in this case as you wished.