Simply
`(a^(p)/a^(q))^(p+q-r).(a^(q)/a^(r ))^(q+r-p).(a^(r )/a^(p))^(r+p-q)`

Find the value of (a^(p)/a^(q))^(p+q-r)xx(a^(r)/a^(p))^(r+p-q)xx(a^(q)/a^(r))^(q+r-p)

((a^(p))/(a^(q)))^(p+q)times((a^(q))/(a^(r)))^(q+r)times((a^(r))/(a^(p)))^(r+p)

((x^(p))/(x^(q)))^((p+q))((x^(q))/(x^(r)))^((q+r))((x^(r))/(x^(p)))^((r+p))

On simplification (a^p/a^q)^(p+q) xx(a^q/a^r)^(q+r)xx(a^r/a^p)^(r+p) yeilds

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1

a^(p-q) . a^(q-r) . a^(r-p) = _____________

(2) If a=x^(q+r)*y^(p) , b=x^(r+p)*y^(q) , c=x^(p+q)y^(r) , show that a^(q-r)b^(r-p)c^(p-q)=1