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

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

Avaliar

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

Passos Para a Resolução

Para multiplicar as potências da mesma base, some os seus expoentes. Some 11 e -31 para obter -20.

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

Para multiplicar as potências da mesma base, some os seus expoentes. Some -20 e -27 para obter -47.

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

Para dividir as potências da mesma base, subtraia o exponente do denominador do exponente do numerador.

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

Calcule 10 elevado a 56 e obtenha 100000000000000000000000000000000000000000000000000000000.

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

Multiplique 9 e 100000000000000000000000000000000000000000000000000000000 para obter 900000000000000000000000000000000000000000000000000000000.

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

Calcule 10 elevado a -19 e obtenha \frac{1}{10000000000000000000}.

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

Multiplique 16 e \frac{1}{10000000000000000000} para obter \frac{1}{625000000000000000}.

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

Calcule \frac{1}{625000000000000000} elevado a 2 e obtenha \frac{1}{390625000000000000000000000000000000}.

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

Multiplique 900000000000000000000000000000000000000000000000000000000 e \frac{1}{390625000000000000000000000000000000} para obter 2304000000000000000000.

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

Multiplique 91 e 166 para obter 15106.

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

Multiplique 15106 e 667 para obter 10075702.

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

Reduza a fração \frac{2304000000000000000000}{10075702} para os termos mais baixos ao retirar e anular 2.

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

Fatorizar

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