Вычислите: (5^(1/4) : 2^(3/4) - 2^(1/4) : 5^(3/4)) * [tex] \sqrt[4]{10000} [/tex]Желательно с объяснениями. Created by Unknownintellegence. algebra-ru

tex]Желательно с объяснениями...

Unknownintellegence @Unknownintellegence

July 2022 1 28 Report

Вычислите:

(5^(1/4) : 2^(3/4) - 2^(1/4) : 5^(3/4)) * [tex] \sqrt[4]{10000} [/tex]

Желательно с объяснениями

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Regent1828

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$\displaystyle (5^{1/4}:2^{3/4}-2^{1/4}:5^{3/4})* \sqrt[4]{10000}= \\ \\ =( \frac{ \sqrt[4]{5}}{ \sqrt[4]{2^{3}}}- \frac{ \sqrt[4]{2}}{ \sqrt[4]{5^{3}}})* \sqrt[4]{10^{4}}= \frac{\sqrt[4]{5^{4}}-\sqrt[4]{2^{4}}}{\sqrt[4]{2^{3}}*\sqrt[4]{5^{3}}}*10= \\ \\ = \frac{5-2}{\sqrt[4]{10^{3}}}*10=3*10^{4/4-3/4}=3*10^{1/4}=3 \sqrt[4]{10}$

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