उत्तर (4)

समाधान

$\left(\frac{x^{\frac{1}{3}}}{3}+\frac{x^{\frac{-2}{3}}}{18}\right)^{18}$

$t _7={ }^{18} c _6\left(\frac{x^{\frac{1}{3}}}{3}\right)^{12}\left(\frac{x^{\frac{-2}{3}}}{2}\right)^{6}={ }^{18} c _6 \frac{1}{(3)^{12}} \cdot \frac{1}{2^{6}}$

$t _{13}={ }^{18} c _{12}\left(\frac{x^{\frac{1}{3}}}{3}\right)^{6}\left(\frac{x^{\frac{-2}{3}}}{2}\right)^{12}={ }^{18} c _{12} \frac{1}{(3)^{6}} \cdot \frac{1}{2^{12}} \cdot x^{-6}$

$m={ }^{18} c _6 \cdot 3^{-12} \cdot 2^{-6}: n={ }^{18} c _{12} \cdot 2^{-12} \cdot 3^{-6}$

$\left(\frac{n}{m}\right)^{\frac{1}{3}}=\left(\frac{2^{-12} \cdot 3^{-6}}{3^{-12} \cdot 2^{-6}}\right)^{\frac{1}{3}}=\left(\frac{3}{2}\right)^{2}=\frac{9}{4}$