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

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

Avaliar

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

Passos Para a Resolução

Para multiplicar as potências da mesma base, some os seus expoentes. Some -6 e -6 para obter -12.

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

Multiplique c e c para obter c^{2}.

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

Calcule 10 elevado a -12 e obtenha \frac{1}{1000000000000}.

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

Multiplique 5 e \frac{1}{1000000000000} para obter \frac{1}{200000000000}.

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

Multiplique \frac{1}{200000000000} e 9 para obter \frac{9}{200000000000}.

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

Multiplique 4 e 10006 para obter 40024.

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

Multiplique 40024 e 8854 para obter 354372496.

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

Calcule 10 elevado a -12 e obtenha \frac{1}{1000000000000}.

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

Multiplique 354372496 e \frac{1}{1000000000000} para obter \frac{22148281}{62500000000}.

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

Multiplique \frac{22148281}{62500000000} e 15 para obter \frac{66444843}{12500000000}.

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

Multiplique \frac{66444843}{12500000000} vezes \frac{c^{2}}{Nm^{2}} ao multiplicar o numerador vezes o numerador e o denominador vezes o denominador.

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

Expresse \frac{66444843c^{2}}{12500000000Nm^{2}}m como uma fração única.

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

Anule m no numerador e no denominador.

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

Expresse \frac{66444843c^{2}}{12500000000Nm}\pi como uma fração única.

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

Divida \frac{9}{200000000000}c^{2} por \frac{66444843c^{2}\pi }{12500000000Nm} ao multiplicar \frac{9}{200000000000}c^{2} pelo recíproco de \frac{66444843c^{2}\pi }{12500000000Nm}.

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

Anule c^{2} no numerador e no denominador.

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

Multiplique \frac{9}{200000000000} e 12500000000 para obter \frac{9}{16}.

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

Calcular a diferenciação com respeito a N

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