Question

how to solve this problem in simple method
​

Answer 1

solution

$( \frac{x {}^{b} }{x {}^{c} } ) {}^{ \frac{1}{bc} } \times ( \frac{x {}^{c} }{x {}^{a} } ) { }^{ \frac{1}{ca} } \times (\frac{x {}^{a} }{x {}^{b} } ) {}^{ \frac{1}{ab} } \\ = x {}^{ \frac{b - c}{bc} } \times x {}^{ \frac{c - a}{ca} } \times x {}^{ \frac{a - b}{ab} } \\ = x {}^{ \frac{b - c}{bc} + \frac{c - a}{ca} + \frac{a - b}{ab} } \\ = x {}^{ \frac{a(b - c) + b(c - a) + c(a - b)}{abc} } \\ = x {}^{ \frac{ab - ac + bc - ab + ac - bc}{abc} } \\ = x {}^{ \frac{0}{abc} } \\ = x {}^{0} \\ = 1$

Answer 2

Answer:

$\huge\begin{lgathered}( \huge\frac{x {}^{b} }{x {}^{c} } ) {}^{ \huge\frac{1}{bc} } \times ( \huge\frac{x {}^{c} }{x {}^{a} } ) { }^{ \huge\frac{1}{ca} } \times (\huge\frac{x {}^{a} }{x {}^{b} } ) {}^{ \huge\frac{1}{ab} } \\ = x {}^{ \huge\frac{b - c}{bc} } \times x {}^{ \huge\frac{c - a}{ca} } \times x {}^{ \huge\frac{a - b}{ab} } \\ = x {}^{ \huge\frac{b - c}{bc} + \frac{c - a}{ca} + \frac{a - b}{ab} } \\ = x {}^{ \huge\frac{a(b - c) + b(c - a) + c(a - b)}{abc} } \\ = x {}^{ \huge\frac{ab - ac + bc - ab + ac - bc}{abc} } \\ = x {}^{ \huge\frac{0}{abc} } \\ = x {}^{0} \\ = 1\end{lgathered}$