## College Algebra 7th Edition

$\dfrac{1}{10\sqrt{10}}$
RECALL: (i) $a^{\frac{m}{n}} =\sqrt[n]{a^m}$ (i) $a^{-m} = \dfrac{1}{a^m}, a\ne0$ Use rule (ii) above to obtain: $=\dfrac{1}{a^{\frac{3}{2}}}$ Use rule (i) above, where m=3 and n=2, to obtain: $=\dfrac{1}{\sqrt{10^3}}$ Factor the radicand so that one factor is a square, then simplify to obtain: $=\dfrac{1}{\sqrt{10^2 \cdot 10}} \\=\dfrac{1}{10\sqrt{10}}$