Try searching in Google.

l hope you will find the answer there.

[tex]\huge\mathcal{\fcolorbox{yellow} {beige} {\orange{ᏗᏁᏕᏇᏋᏒ}}}[/tex]

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[tex] \tt \: \left(\dfrac{x^a}{x^b}\right)^c \times \left(\dfrac{x^b}{x^c}\right)^a \times \left(\dfrac{x^c}{x^a}\right)^b[/tex]

[tex] \tt \: \left(x^{a - b}\right)^c \times \left(x^{b - c}\right)^a \times \left(x^{c - a}\right)^b[/tex]

[tex] \tt \: x^{c(a - b)} \times x^{a(b - c)} \times x^{b(c - a)}[/tex]

[tex] \tt \: x^{c(a - b) + a(b - c) + b(c - a)}[/tex]

c(a - b) + a(b - c) + b(c - a) = 0

x⁰ = 1

hence proved,

[tex]{ \red{ \boxed{ \tt \: \left(\dfrac{x^a}{x^b}\right)^c \times \left(\dfrac{x^b}{x^c}\right)^a \times \left(\dfrac{x^c}{x^a}\right)^b = 1}}}[/tex]

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[tex]{ \orange{ \sf \: hope \: it \: helps \: you}}[/tex]