Answer
$q^{2}r^{5}s\sqrt[7] (q^{3}r^{5})$
Work Step by Step
$\sqrt[7] (q^{17}r^{40}s^{7})=\sqrt[7] (q^{14}\times r^{35}\times s^{7}\times q^{3}r^{5})=\sqrt[7] (q^{14})\times \sqrt[7] (r^{35}) \times \sqrt[7] (s^{7})\times \sqrt[7] (q^{3}r^{5})=q^{2}r^{5}s\sqrt[7] (q^{3}r^{5})$
$\sqrt[7] (q^{14})=q^{2}$, because $(q^{2})^{7}=q^{2\times7}=q^{14}$
$\sqrt[7] (r^{35})=r^{5}$, because $(r^{5})^{7}=r^{5\times7}=r^{35}$
$\sqrt[7] (s^{7})=s$, because $(s)^{7}=s^{7}$
