If p = x^{m + n}.y^l, q = x^{n + l}.y^m and r = x^{l + m}.yⁿ, prove that

p^{m - n}.q^{n - l}.r^{l - m} = 1

Substituting value of p, q and r in p^{m - n}.q^{n - l}.r^{l - m} = 1.

= (x^{m + n}.y^l)^{m - n}.(x^{n + l}.y^m)^{n - l}.(x^{l + m}.yⁿ)^{l - m}

= x^{(m + n)(m - n)}.y^{l(m - n)}.x^{(n + l)(n - l)}.y^{m(n - l)}.x^{(l + m)(l - m)}.y^{n(l - m)}

= x^{m2 - n2}.x^{n2 - l2}.x^{l2 - m2}.y^{lm - ln}.y^{mn - ml}.y^{nl - nm}

= x^{m2 - n2 + n2 - l2 + l2 - m2}.y^{lm - ln + mn - ml + nl - nm}

= x⁰.y⁰

= 1.1

= 1.

Hence, proved that, p^{m - n}.q^{n - l}.r^{l - m} = 1.