Induction Proof Verification

Question

I want to prove that $x^{2n}=(-x)^{2n}$. Here is my attempt, is this correct? Step 1. $x^{2(1)}=(-x)^{2(1)}$ Which is true Step 2. Assume: $x^{2k}=(-x)^{2k}$ Step 3. Proving $x^{2(k+1)}=(-x)^{2(k+1)}$ $x^{2(k+1)}= x^{2k+2}=x^{2k}x^{2}=(-x)^{2k}x^{2}=(-x)^{2k+2}=(-x)^{2(k+1)} $

Answer 1

correction $x^{2(k+1)}=x^{2k+2}=x^{2k}x^{2}=(-x)^{2k}(-x)^{2}=(-x)^{2k+2}=(-x)^{2(k+1)}$

same way you would show $(x+5)^{k+1}=(x+5)^{k}(x+5)$

this step doesn't prove anything $(-x)^{2k}x^{2}=(-x)^{2k+2}$