Ta có
$\sqrt{a.\sqrt[3]{a^2.\sqrt[4]{\dfrac{1}{a}}}} = \sqrt{a.\sqrt[3]{a^2.\sqrt[4]{a^{-1}}}}$
$= \sqrt{a.\sqrt[3]{a^2.a^{-\dfrac{1}{4}}}}$
$= \sqrt{a.\sqrt[3]{a^{\dfrac{7}{4}}}}$
$=\sqrt{a.a^{\dfrac{7}{12}}}$
$= \sqrt{a^{\dfrac{19}{12}}}$
$= a^{\dfrac{19}{24}}$
và $\sqrt[24]{a^7} = a^{\dfrac{7}{24}}$
Vậy ta có
$P = a^{\dfrac{19}{24}} : a^{\dfrac{7}{24}}$
$= a^{\dfrac{19}{24}-\dfrac{7}{24}}$
$= a^{\dfrac{1}{2}}$
Đáp án là B
