Question

x^(a - b) . x^(b - c) . x^(c - a)​

Answer 1

{x}^{a - b} \times {x}^{b - c} \times {x}^{c - a} = 1xa−b×xb−c×xc−a=1

We know that,

{a}^{m} \times {a}^{n} = {a}^{m + n}am×an=am+n

\begin{gathered} {x}^{a - b + b - c + c - a} = 1 \\ \\ {x}^{0} = 1 \\ \end{gathered}xa−b+b−c+c−a=1x0=1

We know that anything with power 0 equals 1

1 = 11=1

Hence proved.