解決1989100^24div1.5^8 |Microsoft數學求解器

$${ 1989100 }^{ 24 } \div { 1.5 }^{ 8 }$$

評估

$$\frac{3767027431078649040458391848510169684094557347288307860202608027854813138496729263089401226825123259638016000000000000000000000000000000000000000000000000}{6561}\approx 5.741544629 \cdot 10^{149}$$

解題步驟

計算 1989100 的 24 乘冪，然後得到 14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000。

$$\frac{14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000}{1.5^{8}}$$

計算 1.5 的 8 乘冪，然後得到 25.62890625。

$$\frac{14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000}{25.62890625}$$

同時對分子與分母乘上 100000000 以展開 \frac{14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000}{25.62890625}。

$$\frac{1471495090265097281429059315824285032849436463784495257891643760880786382225284868394297354228563773296100000000000000000000000000000000000000000000000000000000}{2562890625}$$

透過找出與消去 390625，對分式 \frac{1471495090265097281429059315824285032849436463784495257891643760880786382225284868394297354228563773296100000000000000000000000000000000000000000000000000000000}{2562890625} 約分至最低項。

$$\frac{3767027431078649040458391848510169684094557347288307860202608027854813138496729263089401226825123259638016000000000000000000000000000000000000000000000000}{6561}$$

因式分解

$$\frac{2 ^ {56} \cdot 5 ^ {48} \cdot 19891 ^ {24}}{3 ^ {8}} = 5.741544628987424 \times 10^{149}\frac{4993}{6561} = 5.741544628987424 \times 10^{149}$$