Question

Show that:

`(("x"^"a")/"x"^(-"b"))^("a"-"b").(("x"^"b")/"x"^(-"c"))^("b"-"c").(("x"^"c")/("x"^(-"a")))^("c"-"a")=1`

Answer 1

`"L" . "H" ."S".`

`(("x"^"a")/"x"^(-"b"))^("a"-"b").(("x"^"b")/"x"^(-"c"))^("b"-"c").(("x"^"c")/("x"^(-"a")))^("c"-"a")=1`

`=("x"^("a"+"b"))^("a"-"b").("x"^("b"+"c"))^("b"-"c").("x"^("c"+"a"))^("c"-"a")`

`="x"^("a"^2-"b"^2)."x"^("b"^2-"c"^2)."x"^("c"^2-"a"^2)`

`="x"^("a"^2-"b"^2+"b"^2-"c"^2+"c"^2-"a"^2`

`="x"^0`

`=1 ="R"."H"."S".`