Resolver 1.38*10^-23*27.15/sqrt{2*pi*(3.5*10^-10)^2*101*10^5}=

$$\frac { 1.38 \times 10 ^ { - 23 } \times 27.15 } { \sqrt { 2 } \times \pi \times ( 3.5 \times 10 ^ { - 10 } ) ^ { 2 } \times 101 \times 10 ^ { 5 } } =$$

Calcular

$$\frac{37467\sqrt{2}}{247450000000000\pi }\approx 6.815953004 \cdot 10^{-11}$$

Pasos da solución

Para dividir potencias da mesma base, resta o expoñente do numerador ao expoñente do denominador.

$$\frac{1.38\times 27.15}{101\pi \sqrt{2}\times 10^{28}\times \left(3.5\times 10^{-10}\right)^{2}}$$

Multiplica 1.38 e 27.15 para obter 37.467.

$$\frac{37.467}{101\pi \sqrt{2}\times 10^{28}\times \left(3.5\times 10^{-10}\right)^{2}}$$

Calcula 10 á potencia de 28 e obtén 10000000000000000000000000000.

$$\frac{37.467}{101\pi \sqrt{2}\times 10000000000000000000000000000\times \left(3.5\times 10^{-10}\right)^{2}}$$

Multiplica 101 e 10000000000000000000000000000 para obter 1010000000000000000000000000000.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(3.5\times 10^{-10}\right)^{2}}$$

Calcula 10 á potencia de -10 e obtén \frac{1}{10000000000}.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(3.5\times \frac{1}{10000000000}\right)^{2}}$$

Multiplica 3.5 e \frac{1}{10000000000} para obter \frac{7}{20000000000}.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \left(\frac{7}{20000000000}\right)^{2}}$$

Calcula \frac{7}{20000000000} á potencia de 2 e obtén \frac{49}{400000000000000000000}.

$$\frac{37.467}{1010000000000000000000000000000\pi \sqrt{2}\times \frac{49}{400000000000000000000}}$$

Multiplica 1010000000000000000000000000000 e \frac{49}{400000000000000000000} para obter 123725000000.

$$\frac{37.467}{123725000000\pi \sqrt{2}}$$

Racionaliza o denominador de \frac{37.467}{123725000000\pi \sqrt{2}} mediante a multiplicación do numerador e o denominador por \sqrt{2}.

$$\frac{37.467\sqrt{2}}{123725000000\pi \left(\sqrt{2}\right)^{2}}$$

O cadrado de \sqrt{2} é 2.

$$\frac{37.467\sqrt{2}}{123725000000\pi \times 2}$$

Multiplica 123725000000 e 2 para obter 247450000000.

$$\frac{37.467\sqrt{2}}{247450000000\pi }$$