Question

The value of $(4096{)}^{{\left(\frac{1}{\sqrt{3}}\right)}^{(\sqrt{2}{)}^2}}$ is ___.

• A. 8
• B. 16
• C. 24
• D. 32

Answer 1

The correct option is B

16

$(4096{)}^{{\left(\frac{1}{\sqrt{3}}\right)}^{(\sqrt{2}{)}^2}}$
$=(4096{)}^{{\left(\frac{1}{\sqrt{3}}\right)}^2}$
$=(4096{)}^{\frac{1}{3}}$
$\begin{array}{cc}& \\ 2& 4096\\ 2& 2048\\ 2& 1024\\ 2& 512\\ 2& 256\\ 2& 128\\ 2& 64\\ 2& 32\\ 2& 16\\ 2& 8\\ 2& 4\\ & 2\end{array}$
$\Rightarrow \sqrt[3]{34096}=2\times 2\times 2\times 2=16$