Riješi frac{9*10^{8}*(16*10^{-19})^2}{667*10^-11*91*10^-31*166*10^-27}

$$\frac { 9 \times 10 ^ { 8 } \times ( 16 \times 10 ^ { - 19 } ) ^ { 2 } } { 667 \times 10 ^ { - 11 } \times 91 \times 10 ^ { - 31 } \times 166 \times 10 ^ { - 27 } }$$

Izračunaj

$$\frac{1152000000000000000000000000000000000000000}{5037851}\approx 2,286689305 \cdot 10^{35}$$

Koraci rješenja

Da biste pomnožili potencije s istom bazom, zbrojite eksponente. Dodajte -11 i -31 da biste dobili -42.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-42}\times 91\times 166\times 10^{-27}}$$

Da biste pomnožili potencije s istom bazom, zbrojite eksponente. Dodajte -42 i -27 da biste dobili -69.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-69}\times 91\times 166}$$

Da biste podijelili potencije s istom bazom, oduzmite eksponent nazivnika od eksponenta brojnika.

$$\frac{9\times 10^{77}\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Izračunajte koliko je 77 na 10 da biste dobili 100000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Pomnožite 9 i 100000000000000000000000000000000000000000000000000000000000000000000000000000 da biste dobili 900000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Izračunajte koliko je -19 na 10 da biste dobili \frac{1}{10000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{91\times 166\times 667}$$

Pomnožite 16 i \frac{1}{10000000000000000000} da biste dobili \frac{1}{625000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{91\times 166\times 667}$$

Izračunajte koliko je 2 na \frac{1}{625000000000000000} da biste dobili \frac{1}{390625000000000000000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{91\times 166\times 667}$$

Pomnožite 900000000000000000000000000000000000000000000000000000000000000000000000000000 i \frac{1}{390625000000000000000000000000000000} da biste dobili 2304000000000000000000000000000000000000000.

$$\frac{2304000000000000000000000000000000000000000}{91\times 166\times 667}$$

Pomnožite 91 i 166 da biste dobili 15106.

$$\frac{2304000000000000000000000000000000000000000}{15106\times 667}$$

Pomnožite 15106 i 667 da biste dobili 10075702.

$$\frac{2304000000000000000000000000000000000000000}{10075702}$$

Skratite razlomak \frac{2304000000000000000000000000000000000000000}{10075702} na najmanje vrijednosti tako da izlučite i poništite 2.

$$\frac{1152000000000000000000000000000000000000000}{5037851}$$

Faktor

$$\frac{2 ^ {46} \cdot 3 ^ {2} \cdot 5 ^ {39}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 2,2866893046261194 \times 10^{35}\frac{336198}{5037851} = 2,2866893046261194 \times 10^{35}$$