1. Simplify. \( \begin{array}{ll}\text { a) }(\sqrt{26})^{2} & \text { b) }(\sqrt{1200})^{2} \\ \text { e) }(\sqrt[3]{125000})^{3} & \text { f) }(\sqrt[5]{32})^{5}\end{array} \)

For part a, \( (\sqrt{26})^{2} = 26 \) because squaring a square root simply returns the original number. For part b, \( (\sqrt{1200})^{2} = 1200 \) for the same reason, as squaring the square root cancels out, leaving the original value. Moving on to e, \( (\sqrt[3]{125000})^{3} = 125000 \). This follows the same rule: raising a cube root to the third power returns the original number. Finally, for f, \( (\sqrt[5]{32})^{5} = 32 \), as the fifth root raised to the fifth power reveals the original number once again. In all cases, the process of reversing the root with the corresponding power yields the value inside.