Evaluate the experssion of Power of Power

on

 Question:

$\sqrt[6]{\frac{1}{2}}\sqrt[6]{128}$

Solution:

Remember,  $\sqrt[a]{c}\sqrt[a]{d} = \sqrt[a]{cd}$

So, $\sqrt[6]{\frac{1}{2}}.\sqrt[5]{128}$

  $=\sqrt[6]{\frac{1}{2}.{128}}$

  $= \sqrt[6]{64}$

  We know, 64 = 2.2.2.2.2.2 = $2^{6}$ 

  $= \sqrt[6]{2^{6}}$

  $= 2^{\frac{6}{6}}$

  $= 2^{1}$

  $= 2$



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