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

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

((a^(9))/(a^(r)))^(p)xx((a^(r))/(a^(p)))^(q)xx((a^(p))/(a^(q)))^(r)=1

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)

.prove that (a^(p+q))^(2)(a^(q+r))^(2)(a^(r+p))^(2)/((a^(p)*a^(q)*a^(r))^(4))=1

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

(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

If (log x)/(q-r)=(log y)/(r-p)=(log z)/(p-q) prove that x^(q+r)*y^(r+p)*z^(p+q)=x^(p)*y^(q).z^(r)

Factorize : p^(3)(q-r)^(3)+q^(3)(r-p)^(3)+r^(3)(p-q)^(3)