Exponential relation of GP terms

In a geometric progression, let the $p^{\text{th}}$, $q^{\text{th}}$, and $r^{\text{th}}$ terms be $a$, $b$, and $c$ respectively. Prove that $a^{q-r}{b}^{r-p}{c}^{p-q}=1$.

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. V. Geometrical Progression, Examples V.a, No. 27