حل 1989100^24div1.5^8

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

تقييم

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

خطوات الحل

احسب 1989100 بالأس 24 لتحصل على 14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000.

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

احسب 1.5 بالأس 8 لتحصل على 25.62890625.

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

يمكنك توسيع \frac{14714950902650972814290593158242850328494364637844952578916437608807863822252848683942973542285637732961000000000000000000000000000000000000000000000000}{25.62890625} بضرب كل من البسط والمقام في 100000000.

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

اختزل الكسر \frac{1471495090265097281429059315824285032849436463784495257891643760880786382225284868394297354228563773296100000000000000000000000000000000000000000000000000000000}{2562890625} إلى أبسط قيمة من خلال استخراج 390625 وشطبه.

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

تحليل العوامل

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