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Question Number 185422 by Ml last updated on 21/Jan/23

Answered by hmr last updated on 21/Jan/23

$$2\sqrt{5}=\sqrt{20}={\left(20\right)}^{\frac{1}{2}}$$$$\to a=\sqrt[5]{2\sqrt{5}}=\sqrt[5]{{\left(20\right)}^{\frac{1}{2}}}={\left(20\right)}^{\frac{1}{10}}$$$$$$$$\sqrt[3]{a^{16}}=a^{\frac{16}{3}}={\left({\left(20\right)}^{\frac{1}{10}}\right)}^{\frac{16}{3}}={\left(20\right)}^{\frac{8}{15}}$$$$=\sqrt[15]{{20}^8}$$

Commented by Frix last updated on 21/Jan/23

$$\mathrm{Typo}\mathrm{in}\mathrm{line}3$$

Commented by hmr last updated on 21/Jan/23

$$yessir,thankyou.$$$$Iwilleditit.$$

Answered by Frix last updated on 21/Jan/23

$$a=2^{\frac{1}{5}}{5}^{\frac{1}{10}}$$$$a^{\frac{16}{3}}=2^{\frac{16}{15}}{5}^{\frac{8}{15}}={20}^{\frac{8}{15}}$$

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