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

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

Процени

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

Чекори за решение

За да множите степени со иста основа, соберете ги нивните степенови показатели. Соберете ги -11 и -31 за да добиете -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 множите степени со иста основа, соберете ги нивните степенови показатели. Соберете ги -42 и -27 за да добиете -69.

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

За да делите степени со иста основа, одземете го степеновиот показател на именителот од степеновиот показател на броителот.

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

Пресметајте колку е 10 на степен од 77 и добијте 100000000000000000000000000000000000000000000000000000000000000000000000000000.

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

Помножете 9 и 100000000000000000000000000000000000000000000000000000000000000000000000000000 за да добиете 900000000000000000000000000000000000000000000000000000000000000000000000000000.

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

Пресметајте колку е 10 на степен од -19 и добијте \frac{1}{10000000000000000000}.

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

Помножете 16 и \frac{1}{10000000000000000000} за да добиете \frac{1}{625000000000000000}.

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

Пресметајте колку е \frac{1}{625000000000000000} на степен од 2 и добијте \frac{1}{390625000000000000000000000000000000}.

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

Помножете 900000000000000000000000000000000000000000000000000000000000000000000000000000 и \frac{1}{390625000000000000000000000000000000} за да добиете 2304000000000000000000000000000000000000000.

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

Помножете 91 и 166 за да добиете 15106.

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

Помножете 15106 и 667 за да добиете 10075702.

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

Намалете ја дропката \frac{2304000000000000000000000000000000000000000}{10075702} до најниските услови со извлекување и откажување на 2.

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

Фактор

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