Решете frac{9*10^{8}*(16*10^{-19})^2}{667*10^-11*91*10^-31*166*10^-27}

$$\frac { 9 \times 10 ^ { 8 } \times ( 16 \times 10 ^ { - 19 } ) ^ { 2 } } { 667 \times 10 ^ { - 11 } \times 91 \times 10 ^ { - 31 } \times 166 \times 10 ^ { - 27 } }$$

Изчисляване

$$\frac{1152000000000000000000000000000000000000000}{5037851}\approx 2,286689305 \cdot 10^{35}$$

Стъпки на решението

За да умножите степени с една и съща основа, съберете техните експоненти. Съберете -11 и -31, за да получите -42.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-42}\times 91\times 166\times 10^{-27}}$$

За да умножите степени с една и съща основа, съберете техните експоненти. Съберете -42 и -27, за да получите -69.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-69}\times 91\times 166}$$

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

$$\frac{9\times 10^{77}\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Изчислявате 77 на степен 10 и получавате 100000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Умножете 9 по 100000000000000000000000000000000000000000000000000000000000000000000000000000, за да получите 900000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

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

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{91\times 166\times 667}$$

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

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{91\times 166\times 667}$$

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

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{91\times 166\times 667}$$

Умножете 900000000000000000000000000000000000000000000000000000000000000000000000000000 по \frac{1}{390625000000000000000000000000000000}, за да получите 2304000000000000000000000000000000000000000.

$$\frac{2304000000000000000000000000000000000000000}{91\times 166\times 667}$$

Умножете 91 по 166, за да получите 15106.

$$\frac{2304000000000000000000000000000000000000000}{15106\times 667}$$

Умножете 15106 по 667, за да получите 10075702.

$$\frac{2304000000000000000000000000000000000000000}{10075702}$$

Намаляване на дробта \frac{2304000000000000000000000000000000000000000}{10075702} до най-малките членове чрез извличане на корен и съкращаване на 2.

$$\frac{1152000000000000000000000000000000000000000}{5037851}$$

Разлагане на множители

$$\frac{2 ^ {46} \cdot 3 ^ {2} \cdot 5 ^ {39}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 2,2866893046261194 \times 10^{35}\frac{336198}{5037851} = 2,2866893046261194 \times 10^{35}$$