| Heir of Ramanujan |
25 พฤษภาคม 2008 00:52 |
$\sqrt[39]{\left\{a^{3}b^{2}c\sqrt[3]{abc\sqrt[4]{a^{-1}b^{-2}c^{-3}}}\right\}^{36}}$
$= \left\{a^{3}b^{2}c\sqrt[3]{abc\cdot a^{-\frac{1}{4}}b^{-\frac{2}{4}}c^{-\frac{3}{4}}}\right\}^{\frac{36}{39}}$
$= \left\{a^{3}b^{2}c\sqrt[3]{a^{\frac{3}{4}}b^{\frac{1}{2}}c^{\frac{1}{4}}}\right\}^{\frac{12}{13}}$
$= \left\{a^{3}b^{2}c\cdot a^{\frac{1}{4}}b^{\frac{1}{6}}c^{\frac{1}{12}}\right\}^{\frac{12}{13}}$
$= \left\{a^{\frac{13}{4}}b^{\frac{13}{6}}c^{\frac{13}{12}}\right\}^{\frac{12}{13}}$
$= a^{3}b^{2}c$
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