Prove: \(\left(\frac{x^a}{x^b}\right)^c \times \left(\frac{x^b}{x^c}\right)^a \times \left(\frac{x^c}{x^a}\right)^b = 1\)
Proof
\[ = \left(x^{a-b}\right)^c \cdot \left(x^{b-c}\right)^a \cdot \left(x^{c-a}\right)^b \]
\[ = x^{(a-b)c} \cdot x^{(b-c)a} \cdot x^{(c-a)b} \]
\[ = x^{ac – bc + ab – ac + bc – ab} \]
\[ = x^0 \]
\[ = 1 \]