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

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

Calcula

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

Passos de solució

Per dividir potències de la mateixa base, resteu l'exponent del numerador de l'exponent del denominador.

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

Multipliqueu 138 per 2715 per obtenir 374670.

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

Calculeu 10 elevat a 28 per obtenir 10000000000000000000000000000.

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

Multipliqueu 101 per 10000000000000000000000000000 per obtenir 1010000000000000000000000000000.

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

Calculeu 10 elevat a -10 per obtenir \frac{1}{10000000000}.

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

Multipliqueu 35 per \frac{1}{10000000000} per obtenir \frac{7}{2000000000}.

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

Calculeu \frac{7}{2000000000} elevat a 2 per obtenir \frac{49}{4000000000000000000}.

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

Multipliqueu 1010000000000000000000000000000 per \frac{49}{4000000000000000000} per obtenir 12372500000000.

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

Racionalitzeu el denominador de \frac{374670}{12372500000000\pi \sqrt{2}} multiplicant el numerador i el denominador per \sqrt{2}.

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

L'arrel quadrada de \sqrt{2} és 2.

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

Anul·leu 10 tant al numerador com al denominador.

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

Multipliqueu 2 per 1237250000000 per obtenir 2474500000000.

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