Решете 1989100^24div15^8

$${ 1989100 }^{ 24 } \div { 15 }^{ 8 }$$

Изчисляване

$$\frac{37670274310786490404583918485101696840945573472883078602026080278548131384967292630894012268251232596380160000000000000000000000000000000000000000}{6561}\approx 5,741544629 \cdot 10^{141}$$

Стъпки на решението

Изчислявате 24 на степен 1989100 и получавате 14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000.

$$\frac{14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000}{15^{8}}$$

Изчислявате 8 на степен 15 и получавате 2562890625.

$$\frac{14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000}{2562890625}$$

Намаляване на дробта \frac{14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000}{2562890625} до най-малките членове чрез извличане на корен и съкращаване на 390625.

$$\frac{37670274310786490404583918485101696840945573472883078602026080278548131384967292630894012268251232596380160000000000000000000000000000000000000000}{6561}$$

Разлагане на множители

$$\frac{2 ^ {48} \cdot 5 ^ {40} \cdot 19891 ^ {24}}{3 ^ {8}} = 5,741544628987423 \times 10^{141}\frac{6548}{6561} = 5,741544628987423 \times 10^{141}$$