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

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

Procijeni

$$\frac{1152000000000000000000}{5037851}\approx 2,286689305 \cdot 10^{14}$$

Koraci za rješenje

Da biste pomnožili stepene iste osnove, saberite eksponente. Saberite 11 i -31 da biste dobili -20.

$$\frac{9\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-20}\times 91\times 166\times 10^{-27}}$$

Da biste pomnožili stepene iste osnove, saberite eksponente. Saberite -20 i -27 da biste dobili -47.

$$\frac{9\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-47}\times 91\times 166}$$

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

$$\frac{9\times 10^{56}\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Izračunajte 10 stepen od 56 i dobijte 100000000000000000000000000000000000000000000000000000000.

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Pomnožite 9 i 100000000000000000000000000000000000000000000000000000000 da biste dobili 900000000000000000000000000000000000000000000000000000000.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Izračunajte 10 stepen od -19 i dobijte \frac{1}{10000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{91\times 166\times 667}$$

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

$$\frac{900000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{91\times 166\times 667}$$

Izračunajte \frac{1}{625000000000000000} stepen od 2 i dobijte \frac{1}{390625000000000000000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{91\times 166\times 667}$$

Pomnožite 900000000000000000000000000000000000000000000000000000000 i \frac{1}{390625000000000000000000000000000000} da biste dobili 2304000000000000000000.

$$\frac{2304000000000000000000}{91\times 166\times 667}$$

Pomnožite 91 i 166 da biste dobili 15106.

$$\frac{2304000000000000000000}{15106\times 667}$$

Pomnožite 15106 i 667 da biste dobili 10075702.

$$\frac{2304000000000000000000}{10075702}$$

Svedite razlomak \frac{2304000000000000000000}{10075702} na najprostije elemente rastavlјanjem i kraćenjem 2.

$$\frac{1152000000000000000000}{5037851}$$

Faktor

$$\frac{2 ^ {25} \cdot 3 ^ {2} \cdot 5 ^ {18}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 228668930462611\frac{4711039}{5037851} = 228668930462611,94$$