Question

The ${100}^{th}$ root of ${10}^{\left({10}^{10}\right)}$ is

• A. ${10}^{8^{10}}$
• B. ${10}^{{10}^8}$
• C. $(\sqrt{10}{)}^{(\sqrt{10}{)}^{10}}$
• D. ${10}^{(\sqrt{\left(10\right)}{)}^{\sqrt{10}}}$

Answer 1

The correct option is B ${10}^{{10}^8}$

${100}^{th}$ root of ${10}^{\left({10}^{10}\right)}$

$=\sqrt[100]{100{10}^{\left({10}^{10}\right)}}$

$={10}^{\frac{\left({10}^{10}\right)}{100}}$

$={10}^{\left({10}^{10-2}\right)}$

$={10}^{{10}^8}$