The $100^{t h}$ root of $10^{(10^{10})}$ is ___.

10^{8^{10}}

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10^{10^{8}}

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(\sqrt{10})^{(\sqrt{10})^{10}}

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10 (\sqrt{(10)})^{\sqrt{10}}

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Solution

The correct option is B $10^{10^{8}}$
$100 t h$ root of $10^{(10^{10})} = (10^{(10^{10})})^{\frac{1}{100}}$

$\Rightarrow 10^{(\frac{10^{10}}{100})} = 10^{(10^{8})}$

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