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You can use the method .full_simplify():

sage: var('a b c')              
(a, b, c)
sage: ex = (a/b)^c - (a^c)/(b^c)
sage: ex.full_simplify()
0

You can use the method .full_simplify():

sage: var('a b c')              
(a, b, c)
sage: ex expression = (a/b)^c - (a^c)/(b^c)
sage: ex.full_simplify()
expression.full_simplify()
0