Question

Prove the following:
(x^a)^b-c x (x^b)^c-a x (x^c)^a-b = 1

Answer 1

L.H.S.
= (x^a)^b-c x (x^b)^c-a x (x^c)^a-b 

= `x^("a"("b"-"c")) xx x^("b"("c"-"a")) xx x^("c"("a"-"b"))`     .....(Using (a^m)ⁿ = a^mn)

= `x^("ab"-"ac") xx x^("bc"-"ab") xx x^("ac"-"bc")`
= `x^("ab"-"ac"+"bc"-"ab"+"ac"-"bc")`     .....(Using a^m x aⁿ = a^m+n)
= x°
=1
= R.H.S
= Hence proved.