Resolver 316*9*10^9left(16*10^-19right)^2/664*10^-27{left(5*{10^7right)}^-2}

$$\frac{ 316 \cdot 9 \times { 10 }^{ 9 } { \left(16 \times { 10 }^{ -19 } \right) }^{ 2 } }{ 664 \times { 10 }^{ -27 } { \left(5 \times { 10 }^{ 7 } \right) }^{ -2 } }$$

Avaliar

$$\frac{2275200000000000000}{83}\approx 2,741204819 \cdot 10^{16}$$

Passos Para a Resolução

Anule 4 no numerador e no denominador.

$$\frac{9\times 79\times 10^{9}\times \left(16\times 10^{-19}\right)^{2}}{166\times 10^{-27}\times \left(5\times 10^{7}\right)^{-2}}$$

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

$$\frac{9\times 79\times 10^{36}\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplique 9 e 79 para obter 711.

$$\frac{711\times 10^{36}\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Calcule 10 elevado a 36 e obtenha 1000000000000000000000000000000000000.

$$\frac{711\times 1000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplique 711 e 1000000000000000000000000000000000000 para obter 711000000000000000000000000000000000000.

$$\frac{711000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

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

$$\frac{711000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

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

$$\frac{711000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

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

$$\frac{711000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Multiplique 711000000000000000000000000000000000000 e \frac{1}{390625000000000000000000000000000000} para obter \frac{45504}{25}.

$$\frac{\frac{45504}{25}}{166\times \left(5\times 10^{7}\right)^{-2}}$$

Calcule 10 elevado a 7 e obtenha 10000000.

$$\frac{\frac{45504}{25}}{166\times \left(5\times 10000000\right)^{-2}}$$

Multiplique 5 e 10000000 para obter 50000000.

$$\frac{\frac{45504}{25}}{166\times 50000000^{-2}}$$

Calcule 50000000 elevado a -2 e obtenha \frac{1}{2500000000000000}.

$$\frac{\frac{45504}{25}}{166\times \frac{1}{2500000000000000}}$$

Multiplique 166 e \frac{1}{2500000000000000} para obter \frac{83}{1250000000000000}.

$$\frac{\frac{45504}{25}}{\frac{83}{1250000000000000}}$$

Divida \frac{45504}{25} por \frac{83}{1250000000000000} ao multiplicar \frac{45504}{25} pelo recíproco de \frac{83}{1250000000000000}.

$$\frac{45504}{25}\times \frac{1250000000000000}{83}$$

Multiplique \frac{45504}{25} e \frac{1250000000000000}{83} para obter \frac{2275200000000000000}{83}.

$$\frac{2275200000000000000}{83}$$

Fatorizar

$$\frac{2 ^ {19} \cdot 3 ^ {2} \cdot 5 ^ {14} \cdot 79}{83} = 27412048192771084\frac{28}{83} = 27412048192771084$$