Монгол Бодлогын Сан

Заавар:Зэргийн чанар ашигла.

Бодолт:\begin{align*} \biggl(\dfrac{81a^{4n-1}}{25b^5}\biggr)^3\cdot\biggl(-\dfrac{5^2\cdot b^3}{27a^{3n-1}}\biggr)^4&=\dfrac{(81a^{4n-1})^3}{(25b^5)^3}\cdot(-1)^4\cdot\dfrac{(5^2b^3)^4}{(27a^{3n-1})^4}\\ &=\dfrac{(3^4a^{4n-1})^3}{(5^2b^5)^3}\cdot(-1)^4\cdot\dfrac{(5^2b^3)^4}{(3^3a^{3n-1})^4}\\ &=\dfrac{3^{12}a^{12n-3}}{5^6b^{15}}\cdot\dfrac{5^8b^{12}}{3^{12}a^{12n-4}}\\ &=3^{12-12}5^{8-6}a^{(12n-3)-(12n-4)}b^{12-15}\\ &=25ab^{-3} \end{align*}