Монгол Бодлогын Сан

Заавар: $\sqrt[n]{a}=a^{\frac1n}$, $(ab)^{n}=a^nb^n$, $(a^m)^n=a^{mn}$, $a^m\cdot a^n=a^{m+n}$, $\dfrac{a^m}{a^n}=a^{m-n}$ болохыг ашигла.

Бодолт: $$\dfrac{(\sqrt[3]{x}\cdot\sqrt[4]{y})^{12}(\sqrt[5]{x}\cdot\sqrt{y})^{10}}{(\sqrt{x}\cdot\sqrt[3]{y})^{18}}=\dfrac{(x^{\frac13}\cdot y^{\frac14})^{12}(x^{\frac15}\cdot y^{\frac12})^{10}}{(x^{\frac12}\cdot y^\frac13)^{18}}=$$ $$=\dfrac{(x^{\frac{12}3}\cdot y^{\frac{12}4})(x^{\frac{10}5}\cdot y^{\frac{10}2})}{(x^{\frac{18}2}\cdot y^\frac{18}3)}=\dfrac{(x^4y^3)(x^2y^5)}{x^9y^6}=\dfrac{x^6y^8}{x^9y^6}=\dfrac{y^2}{x^3}$$