Value of fifth root of 10^{10^{10}} is

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Basic of Logarithms

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The value of the fifth root of $10^{10^{10}}$ is

A

$10^{2 \times 10^9}$

B

$10^{20 \times 10^9}$

C

$10^{10^2}$

D

$10^{2^{10}}$

(KVPY-2021)

Solution

(a)

$\left(10^{10^{10}}\right)^{\frac{1}{5}}$

$=10^{10^{10} \times \frac{1}{5}}=10^{10^9 \times \frac{10}{5}}=10^{2 \times 10^9}$

Standard 11

Mathematics

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