Answer:
Step-by-step explanation:
[tex]a = b^{c}[/tex] ------------(I)
Plug in b = [tex]c^{a}[/tex]
(I) ---> [tex]a = (c^{a})^{c}= \ c^{a*c} = \ c^{ac}[/tex] -----------(II)
Plug in c = [tex]a^{b}[/tex]
(II) ----->
[tex]a = (a^{b})^{ac} \\\\a = a^{ac*b}\\\\a = a^{abc}[/tex]
Both sides base are same. So, compare the powers
1 = abc
abc = 1
Hence proved
