Решете 316*9*10^9left(16*10^-19right)^2/664*10^-27{left(5*{10^7right)}^-2}

$$\frac{ 316 \cdot 9 \times { 10 }^{ 9 } { \left(16 \times { 10 }^{ -19 } \right) }^{ 2 } }{ 664 \times { 10 }^{ -27 } { \left(5 \times { 10 }^{ 7 } \right) }^{ -2 } }$$

Изчисляване

$$\frac{2275200000000000000}{83}\approx 2,741204819 \cdot 10^{16}$$

Стъпки на решението

Съкращаване на 4 в числителя и знаменателя.

$$\frac{9\times 79\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{166\times 10^{-27}\times \left(5\times 10^{7}\right)^{-2}}$$

За да разделите степени с една и съща основа, извадете експонентата на знаменателя от експонентата на числителя.

$$\frac{9\times 79\times 10^{36}\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Умножете 9 по 79, за да получите 711.

$$\frac{711\times 10^{36}\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Изчислявате 36 на степен 10 и получавате 1000000000000000000000000000000000000.

$$\frac{711\times 1000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Умножете 711 по 1000000000000000000000000000000000000, за да получите 711000000000000000000000000000000000000.

$$\frac{711000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Изчислявате -19 на степен 10 и получавате \frac{1}{10000000000000000000}.

$$\frac{711000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Умножете 16 по \frac{1}{10000000000000000000}, за да получите \frac{1}{625000000000000000}.

$$\frac{711000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Изчислявате 2 на степен \frac{1}{625000000000000000} и получавате \frac{1}{390625000000000000000000000000000000}.

$$\frac{711000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Умножете 711000000000000000000000000000000000000 по \frac{1}{390625000000000000000000000000000000}, за да получите \frac{45504}{25}.

$$\frac{\frac{45504}{25}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Изчислявате 7 на степен 10 и получавате 10000000.

$$\frac{\frac{45504}{25}}{166\times \left(5\times 10000000\right)^{-2}}$$

Умножете 5 по 10000000, за да получите 50000000.

$$\frac{\frac{45504}{25}}{166\times 50000000^{-2}}$$

Изчислявате -2 на степен 50000000 и получавате \frac{1}{2500000000000000}.

$$\frac{\frac{45504}{25}}{166\times \frac{1}{2500000000000000}}$$

Умножете 166 по \frac{1}{2500000000000000}, за да получите \frac{83}{1250000000000000}.

$$\frac{\frac{45504}{25}}{\frac{83}{1250000000000000}}$$

Разделете \frac{45504}{25} на \frac{83}{1250000000000000} чрез умножаване на \frac{45504}{25} по обратната стойност на \frac{83}{1250000000000000}.

$$\frac{45504}{25}\times \frac{1250000000000000}{83}$$

Умножете \frac{45504}{25} по \frac{1250000000000000}{83}, за да получите \frac{2275200000000000000}{83}.

$$\frac{2275200000000000000}{83}$$

Разлагане на множители

$$\frac{2 ^ {19} \cdot 3 ^ {2} \cdot 5 ^ {14} \cdot 79}{83} = 27412048192771084\frac{28}{83} = 27412048192771084$$