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

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

Ovrednoti

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

Koraki rešitve

Če želite deliti potence enake osnove, odštejte eksponent števca od eksponenta imenovalca.

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

Pomnožite 138 in 2715, da dobite 374670.

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

Izračunajte potenco 10 števila 28, da dobite 10000000000000000000000000000.

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

Pomnožite 101 in 10000000000000000000000000000, da dobite 1010000000000000000000000000000.

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

Izračunajte potenco 10 števila -10, da dobite \frac{1}{10000000000}.

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

Pomnožite 35 in \frac{1}{10000000000}, da dobite \frac{7}{2000000000}.

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

Izračunajte potenco \frac{7}{2000000000} števila 2, da dobite \frac{49}{4000000000000000000}.

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

Pomnožite 1010000000000000000000000000000 in \frac{49}{4000000000000000000}, da dobite 12372500000000.

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

Racionalizirajte imenovalec \frac{374670}{12372500000000\pi \sqrt{2}} tako, da pomnožite števec in imenovalec s \sqrt{2}.

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

Kvadrat vrednosti \sqrt{2} je 2.

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

Okrajšaj 10 v števcu in imenovalcu.

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

Pomnožite 2 in 1237250000000, da dobite 2474500000000.

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