Simplify and express the result in the form

MATHEMATICS · Single correct · AoPS · Mathematics · Follow the Rules · Follow the Rules

Problem

Simplify

\sqrt{2}\,\times\,\sqrt[4]{8}\,\times\,\sqrt[3]{4}

and express the result in the form

2^{k}

. What is the value of

k

? (a)

\dfrac{19}{12}

(b)

\dfrac{23}{12}

(c)

\dfrac{13}{12}

(d)

\dfrac{17}{12}