Question

If a=xy^(p-1), b=xy^(q-1), c=xy^(r-1), prove that a^(q-r) × b^(r-p) × c^(p-q) = 1

Answer 1

I am pretty sure the you made a slight mistake in typing the question
you would have to prove
$a^{q-r}b^{r-p}c^{p-q} = 1$
so to do that just substitute the values of a b and c
we get
LHS=[tex] x^{q-r+r-p+p-q}y^{(p-1)(q-r) + (q-1)(r-p) + (r-1)(p-q)} [/tex]
$LHS = x^{0}y^{pq-pr-q+r+qr-pq-r+p+pr-qr-p+q} = x^0y^0 = 1 = RHS$

Proved.