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

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

Procijeni

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

Koraci za rješenje

Da biste podijelili stepene iste osnove, oduzmite eksponent brojioca od eksponenta imenioca.

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

Pomnožite 138 i 2715 da biste dobili 374670.

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

Izračunajte 10 stepen od 28 i dobijte 10000000000000000000000000000.

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

Pomnožite 101 i 10000000000000000000000000000 da biste dobili 1010000000000000000000000000000.

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

Izračunajte 10 stepen od -10 i dobijte \frac{1}{10000000000}.

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

Pomnožite 35 i \frac{1}{10000000000} da biste dobili \frac{7}{2000000000}.

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

Izračunajte \frac{7}{2000000000} stepen od 2 i dobijte \frac{49}{4000000000000000000}.

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

Pomnožite 1010000000000000000000000000000 i \frac{49}{4000000000000000000} da biste dobili 12372500000000.

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

Racionalizirajte imenilac broja \frac{374670}{12372500000000\pi \sqrt{2}} tako što ćete pomnožiti brojilac i imenilac sa \sqrt{2}.

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

Kvadrat broja \sqrt{2} je 2.

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

Otkaži 10 u brojiocu i imeniocu.

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

Pomnožite 2 i 1237250000000 da biste dobili 2474500000000.

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