Intermediate Algebra for College Students (7th Edition)

$\sqrt[6]{(x-5)^5}$
RECALL: For nonegative numbers a and b, $\sqrt[n]{a} \cdot \sqrt[n]{b} = \sqrt[n]{ab}$ Also, $(x-c)^{a}+(x-c)^{b}=(x-c)^{ab}$ Use the rules above to obtain: $=\sqrt[6]{(x-5)(x-5)^4} \\=\sqrt[6]{(x-5)^{1+4}} \\=\sqrt[6]{(x-5)^5}$