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$${\frac{{\mathtt{4}}{\mathtt{\,\times\,}}{{\mathtt{2}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{4}}}}\right)}{\mathtt{\,\times\,}}{{\mathtt{8}}}^{\left({\frac{{\mathtt{1}}}{{\mathtt{6}}}}\right)}}{{{\mathtt{16}}}^{\left({\frac{{\mathtt{3}}}{{\mathtt{4}}}}\right)}}}$$

Guest Feb 28, 2015

Best Answer 

 #1
avatar+93683 
+5

Mmm

Lets see.

 

$$\\\dfrac{4\times 2^{1/4}\times8^{1/6}}{16^{3/4}}\\\\\\
=\dfrac{2^2\times 2^{1/4}\times(2^3)^{1/6}}{(2^4)^{3/4}}\\\\\\
=\dfrac{2^2\times 2^{1/4}\times 2^{3/6}}{2^{12/4}}\\\\\\
=\dfrac{2^2\times 2^{0.25}\times 2^{0.5}}{2^{3}}\\\\
=2^{2+0.25+0.5-3}\\\\
=2^{-0.25}\\\\
=\frac{1}{2^{1/4}}\\\\
=\frac{1}{\sqrt[4]{2}}$$

Melody  Feb 28, 2015
 #1
avatar+93683 
+5
Best Answer

Mmm

Lets see.

 

$$\\\dfrac{4\times 2^{1/4}\times8^{1/6}}{16^{3/4}}\\\\\\
=\dfrac{2^2\times 2^{1/4}\times(2^3)^{1/6}}{(2^4)^{3/4}}\\\\\\
=\dfrac{2^2\times 2^{1/4}\times 2^{3/6}}{2^{12/4}}\\\\\\
=\dfrac{2^2\times 2^{0.25}\times 2^{0.5}}{2^{3}}\\\\
=2^{2+0.25+0.5-3}\\\\
=2^{-0.25}\\\\
=\frac{1}{2^{1/4}}\\\\
=\frac{1}{\sqrt[4]{2}}$$

Melody  Feb 28, 2015

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