Resol frac{5*10^{-6}c*9*10^-6c}{4pi*10006*8854*10^-12*c^2/Nm^2*15m}

$$\frac { 5 \cdot 10 ^ { - 6 } c \cdot 9 \cdot 10 ^ { - 6 } c } { 4 \pi \cdot 10006 \cdot 8854 \cdot 10 ^ { - 12 } \cdot \frac { c ^ { 2 } } { N m ^ { 2 } } \cdot 15 m }$$

Calcula

$$\frac{3Nm}{354372496\pi }$$

Passos de solució

Per multiplicar potències de la mateixa base, afegiu-ne els exponents. Afegiu -6 i -6 per obtenir -12.

$$\frac{5\times 10^{-12}c\times 9c}{4\pi \times 10006\times 8854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Multipliqueu c per c per obtenir c^{2}.

$$\frac{5\times 10^{-12}c^{2}\times 9}{4\pi \times 10006\times 8854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Calculeu 10 elevat a -12 per obtenir \frac{1}{1000000000000}.

$$\frac{5\times \frac{1}{1000000000000}c^{2}\times 9}{4\pi \times 10006\times 8854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Multipliqueu 5 per \frac{1}{1000000000000} per obtenir \frac{1}{200000000000}.

$$\frac{\frac{1}{200000000000}c^{2}\times 9}{4\pi \times 10006\times 8854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Multipliqueu \frac{1}{200000000000} per 9 per obtenir \frac{9}{200000000000}.

$$\frac{\frac{9}{200000000000}c^{2}}{4\pi \times 10006\times 8854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Multipliqueu 4 per 10006 per obtenir 40024.

$$\frac{\frac{9}{200000000000}c^{2}}{40024\pi \times 8854\times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Multipliqueu 40024 per 8854 per obtenir 354372496.

$$\frac{\frac{9}{200000000000}c^{2}}{354372496\pi \times 10^{-12}\times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Calculeu 10 elevat a -12 per obtenir \frac{1}{1000000000000}.

$$\frac{\frac{9}{200000000000}c^{2}}{354372496\pi \times \frac{1}{1000000000000}\times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Multipliqueu 354372496 per \frac{1}{1000000000000} per obtenir \frac{22148281}{62500000000}.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{22148281}{62500000000}\pi \times \frac{c^{2}}{Nm^{2}}\times 15m}$$

Multipliqueu \frac{22148281}{62500000000} per 15 per obtenir \frac{66444843}{12500000000}.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843}{12500000000}\pi \times \frac{c^{2}}{Nm^{2}}m}$$

Per multiplicar \frac{66444843}{12500000000} per \frac{c^{2}}{Nm^{2}}, multipliqueu el numerador pel numerador i el denominador pel denominador.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843c^{2}}{12500000000Nm^{2}}\pi m}$$

Expresseu \frac{66444843c^{2}}{12500000000Nm^{2}}m com a fracció senzilla.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843c^{2}m}{12500000000Nm^{2}}\pi }$$

Anul·leu m tant al numerador com al denominador.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843c^{2}}{12500000000Nm}\pi }$$

Expresseu \frac{66444843c^{2}}{12500000000Nm}\pi com a fracció senzilla.

$$\frac{\frac{9}{200000000000}c^{2}}{\frac{66444843c^{2}\pi }{12500000000Nm}}$$

Dividiu \frac{9}{200000000000}c^{2} per \frac{66444843c^{2}\pi }{12500000000Nm} multiplicant \frac{9}{200000000000}c^{2} pel recíproc de \frac{66444843c^{2}\pi }{12500000000Nm}.

$$\frac{\frac{9}{200000000000}c^{2}\times 12500000000Nm}{66444843c^{2}\pi }$$

Anul·leu c^{2} tant al numerador com al denominador.

$$\frac{\frac{9}{200000000000}\times 12500000000Nm}{66444843\pi }$$

Multipliqueu \frac{9}{200000000000} per 12500000000 per obtenir \frac{9}{16}.

$$\frac{\frac{9}{16}Nm}{66444843\pi }$$

Diferencieu N

$$\frac{3m}{354372496\pi }$$