Выполнить действия (a>0, b>0):[tex]6ab \sqrt[9]{{a {}^{8} } b {}^{3}} \div \frac{2a}{3b} \sqrt[6]{{a {}^{2} } b { }^{5}}[/tex]. Created by artemiy17012003. algebra-ru

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artemiy17012003 @artemiy17012003

July 2022 1 5 Report

Выполнить действия (a>0, b>0):
[tex]6ab \sqrt[9]{{a {}^{8} } b {}^{3}} \div \frac{2a}{3b} \sqrt[6]{{a {}^{2} } b { }^{5}}[/tex]

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NNNLLL54

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$1)\; \; a>0\; ,\; \; b>0\\\\6ab\, \sqrt[9]{a^8b^3}:\frac{2a}{3b}\, \sqrt[6]{a^2b^5}=6\cdot a\cdot b\cdot a^{\frac{8}{9}}\cdot b^{\frac{1}{3}}:\frac{2a}{3b}\cdot a^{\frac{1}{3}}\cdot b^{\frac{5}{6}}=\\\\=\frac{6\cdot a\cdot a^{\frac{8}{9}}\cdot b\cdot b^{\frac{1}{3}}}{\frac{2a}{3b}}\cdot a^{\frac{1}{3}}\cdot b^{\frac{5}{6}}=\frac{6\cdot a\cdot a^{\frac{8}{9}}\cdot b\cdot b^{\frac{1}{3}}\cdot 3b}{2a}\cdot a^{\frac{1}{3}}\cdot b^{\frac{5}{6}}=9\cdot a^{\frac{8}{9}}\cdot b^{\frac{7}{3}}\cdot a^{\frac{1}{3}}\cdot b^{\frac{5}{6}}=$

$=9\cdot a^{\frac{11}{9}}\cdot b^{\frac{19}{6}}=9\cdot \sqrt[9]{a^{11}}\cdot \sqrt[6]{b^{19}}$

$2)\; \; a>0\; ,\; \; b>0\\\\\Big (6ab\, \sqrt[9]{a^8b^3}\Big ):\Big (\frac{2a}{3b}\, \sqrt[6]{a^2b^5}\Big )=\Big (6\cdot a\cdot b\cdot a^{\frac{8}{9}}\cdot b^{\frac{1}{3}}\Big ):\Big (\frac{2a\cdot a^{\frac{1}{3}}\cdot b^{\frac{5}{6}}}{3b}\Big )=\\\\=\frac{6\cdot a\cdot a^{\frac{8}{9}}\cdot b\cdot b^{\frac{1}{3}}\cdot 3b}{2a\cdot a^{\frac{1}{3}}\cdot b^{\frac{5}{6}}}=9\cdot a^{\frac{5}{9}}\cdot b^{\frac{3}{2}}=9\cdot \sqrt[9]{a^5}\cdot \sqrt{b^3}$

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