Solution

\[ \begin{aligned} &= \left( \frac{x}{y} \right)^a \times \left( \frac{y}{z} \right)^a \times \left( \frac{z}{x} \right)^a \\ \\ &= \left( \frac{\cancel x}{\cancel y} \times \frac{\cancel y}{\cancel z} \times \frac{\cancel z}{\cancel x} \right)^a \\ \\ &= 1^a \\ &= 1 \end{aligned} \]

Answer \(\displaystyle \left( \frac{x}{y} \right)^a \times \left( \frac{y}{z} \right)^a \times \left( \frac{z}{x} \right)^a= \color{red} 1 \)

Solution

\[ \begin{aligned} & = \left( \frac{x^a}{x^b} \right) \times \left( \frac{x^b}{x^c} \right) \times \left( \frac{x^c}{x^a} \right) \\ \\ &= x^{(a-b)} \times x^{(b-c)} \times x^{(c-a)} \\ \\ &= x^{(a-b) + (b-c) + (c-a)} \\ \\ &= x^{(a-b+b-c+c-a)} \\ \\ &= x^0 \\ \\ &= 1 \end{aligned} \]

Answer \( \displaystyle \left( \frac{x^a}{x^b} \right) \times \left( \frac{x^b}{x^c} \right) \times \left( \frac{x^c}{x^a} \right) = \color{red} 1 \)