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

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

Calcula

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

Passos de solució

Per multiplicar potències de la mateixa base, afegiu-ne els exponents. Afegiu 11 i -31 per obtenir -20.

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

Per multiplicar potències de la mateixa base, afegiu-ne els exponents. Afegiu -20 i -27 per obtenir -47.

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

Per dividir potències de la mateixa base, resteu l'exponent del denominador de l'exponent del numerador.

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

Calculeu 10 elevat a 56 per obtenir 100000000000000000000000000000000000000000000000000000000.

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

Multipliqueu 9 per 100000000000000000000000000000000000000000000000000000000 per obtenir 900000000000000000000000000000000000000000000000000000000.

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

Calculeu 10 elevat a -19 per obtenir \frac{1}{10000000000000000000}.

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

Multipliqueu 16 per \frac{1}{10000000000000000000} per obtenir \frac{1}{625000000000000000}.

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

Calculeu \frac{1}{625000000000000000} elevat a 2 per obtenir \frac{1}{390625000000000000000000000000000000}.

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

Multipliqueu 900000000000000000000000000000000000000000000000000000000 per \frac{1}{390625000000000000000000000000000000} per obtenir 2304000000000000000000.

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

Multipliqueu 91 per 166 per obtenir 15106.

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

Multipliqueu 15106 per 667 per obtenir 10075702.

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

Redueix la fracció \frac{2304000000000000000000}{10075702} al màxim extraient i anul·lant 2.

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

Factoritzar

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