Resolver 138*10^-23*2715/sqrt{2*pi*(35*10^-10)^2*101*10^5}=

$$\frac { 138 \times 10 ^ { - 23 } \times 2715 } { \sqrt { 2 } \times \pi \times ( 35 \times 10 ^ { - 10 } ) ^ { 2 } \times 101 \times 10 ^ { 5 } } =$$

Avaliar

$$\frac{37467\sqrt{2}}{2474500000000\pi }\approx 6,815953004 \cdot 10^{-9}$$

Passos Para a Resolução

Para dividir as potências da mesma base, subtraia o exponente do numerador do exponente do denominador.

$$\frac{138\times 2715}{101\pi \sqrt{2}\times 10^{28}\times \left(35\times 10^{-10}\right)^{2}}$$

Multiplique 138 e 2715 para obter 374670.

$$\frac{374670}{101\pi \sqrt{2}\times 10^{28}\times \left(35\times 10^{-10}\right)^{2}}$$

Calcule 10 elevado a 28 e obtenha 10000000000000000000000000000.

$$\frac{374670}{101\pi \sqrt{2}\times 10000000000000000000000000000\times \left(35\times 10^{-10}\right)^{2}}$$

Multiplique 101 e 10000000000000000000000000000 para obter 1010000000000000000000000000000.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(35\times 10^{-10}\right)^{2}}$$

Calcule 10 elevado a -10 e obtenha \frac{1}{10000000000}.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(35\times \frac{1}{10000000000}\right)^{2}}$$

Multiplique 35 e \frac{1}{10000000000} para obter \frac{7}{2000000000}.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \left(\frac{7}{2000000000}\right)^{2}}$$

Calcule \frac{7}{2000000000} elevado a 2 e obtenha \frac{49}{4000000000000000000}.

$$\frac{374670}{1010000000000000000000000000000\pi \sqrt{2}\times \frac{49}{4000000000000000000}}$$

Multiplique 1010000000000000000000000000000 e \frac{49}{4000000000000000000} para obter 12372500000000.

$$\frac{374670}{12372500000000\pi \sqrt{2}}$$

Racionalize o denominador de \frac{374670}{12372500000000\pi \sqrt{2}} ao multiplicar o numerador e o denominador por \sqrt{2}.

$$\frac{374670\sqrt{2}}{12372500000000\pi \left(\sqrt{2}\right)^{2}}$$

O quadrado de \sqrt{2} é 2.

$$\frac{374670\sqrt{2}}{12372500000000\pi \times 2}$$

Anule 10 no numerador e no denominador.

$$\frac{37467\sqrt{2}}{2\times 1237250000000\pi }$$

Multiplique 2 e 1237250000000 para obter 2474500000000.

$$\frac{37467\sqrt{2}}{2474500000000\pi }$$