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

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

Evaluer

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

Løsningsvejledning

Hvis du vil gange potenser for den samme base, skal du tilføje deres eksponenter. Tilføj -6 og -6 for at få -12.

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

Multiplicer c og c for at få c^{2}.

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

Beregn 10 til potensen af -12, og få \frac{1}{1000000000000}.

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

Multiplicer 5 og \frac{1}{1000000000000} for at få \frac{1}{200000000000}.

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

Multiplicer \frac{1}{200000000000} og 9 for at få \frac{9}{200000000000}.

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

Multiplicer 4 og 10006 for at få 40024.

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

Multiplicer 40024 og 8854 for at få 354372496.

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

Beregn 10 til potensen af -12, og få \frac{1}{1000000000000}.

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

Multiplicer 354372496 og \frac{1}{1000000000000} for at få \frac{22148281}{62500000000}.

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

Multiplicer \frac{22148281}{62500000000} og 15 for at få \frac{66444843}{12500000000}.

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

Multiplicer \frac{66444843}{12500000000} gange \frac{c^{2}}{Nm^{2}} ved at multiplicere tæller gange tæller og nævner gange nævner.

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

Udtryk \frac{66444843c^{2}}{12500000000Nm^{2}}m som en enkelt brøk.

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

Udlign m i både tælleren og nævneren.

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

Udtryk \frac{66444843c^{2}}{12500000000Nm}\pi som en enkelt brøk.

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

Divider \frac{9}{200000000000}c^{2} med \frac{66444843c^{2}\pi }{12500000000Nm} ved at multiplicere \frac{9}{200000000000}c^{2} med den reciprokke værdi af \frac{66444843c^{2}\pi }{12500000000Nm}.

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

Udlign c^{2} i både tælleren og nævneren.

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

Multiplicer \frac{9}{200000000000} og 12500000000 for at få \frac{9}{16}.

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

Differentier w.r.t. N

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