Chapter 7 - Section 7.3 - Simplifying Radical Expressions - Exercise Set: 123

$q^{2}r^{5}s\sqrt[7] (q^{3}r^{5})$

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 $(s)^{7}=s^{7}$

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