Answer
The property was verified for $n=1$.
The property was verified when $n$ was changed by $n+1$.
Work Step by Step
Prove the property for $n=1$
$(x_1)^{-1}=x_1^{-1}$
The property is verified for $n=1$
Assuming that $(x_1x_2x_3...x_n)^{-1}=x_1^{-1}x_2^{-1}x_3^{-1}...x_n^{-1}$ for all integers $n\geq1$, we need to prove that $(x_1x_2x_3...x_nx_{n+1})^{-1}=x_1^{-1}x_2^{-1}x_3^{-1}...x_n^{-1}x_{n+1}^{-1}$:
$(x_1x_2x_3...x_nx_{n+1})^{-1}=(x_1x_2x_3...x_n)^{-1}x_{n+1}^{-1}=x_1^{-1}x_2^{-1}x_3^{-1}...x_n^{-1}x_{n+1}^{-1}$
