√( 10 ^ 10 ^ 10 ) =( 10 ^ 10 ^ 10 ) #160; ^ 1 / 100 #160; = 10 ^ 10 ^ 10 × 1 / 100 #160; = 10 ^ 10 ^ 10 × 1 / 10 ^ 2 #160; ...

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Laws of Exponents for Real Numbers

Evaluate = √...

Question

Evaluate = $\sqrt[100]{10^{10^{10}}}$

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Solution

$\sqrt[100]{10^{10^{10}}} = {(10^{10^{10}})}^{\frac{1}{100}} = 10^{10^{10} \times \frac{1}{100}} = 10^{10^{10} \times \frac{1}{10^{2}}} = 10^{10^{10 - 2}} = 10^{10^{8}} = 10^{100000000} = 100.....100000000$ zeros

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