- Thread starter Mos5180d
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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 whileApply the exponent rule a^(m+n) = a^m * a^n.

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-1 = -1 always. It does NOT depend on the parity of x.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.

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For clarity, I think what you meant was this proof by cases: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

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.