Solucionar 89910^86410^-129610^-16/{left(8210^-4right)^2}

$$\frac{ 899 { 10 }^{ 8 } 64 { 10 }^{ -12 } 96 { 10 }^{ -16 } }{ { \left(82 { 10 }^{ -4 } \right) }^{ 2 } }$$

Calcular

$$\frac{2697}{3283203125000}\approx 8,214538965 \cdot 10^{-10}$$

Pasos de la solución

Para multiplicar potencias de la misma base, sume sus exponentes. Sume 8 y -12 para obtener -4.

$$\frac{899\times 10^{-4}\times 64\times 96\times 10^{-16}}{\left(82\times 10^{-4}\right)^{2}}$$

Para multiplicar potencias de la misma base, sume sus exponentes. Sume -4 y -16 para obtener -20.

$$\frac{899\times 10^{-20}\times 64\times 96}{\left(82\times 10^{-4}\right)^{2}}$$

Calcula 10 a la potencia de -20 y obtiene \frac{1}{100000000000000000000}.

$$\frac{899\times \frac{1}{100000000000000000000}\times 64\times 96}{\left(82\times 10^{-4}\right)^{2}}$$

Multiplica 899 y \frac{1}{100000000000000000000} para obtener \frac{899}{100000000000000000000}.

$$\frac{\frac{899}{100000000000000000000}\times 64\times 96}{\left(82\times 10^{-4}\right)^{2}}$$

Multiplica \frac{899}{100000000000000000000} y 64 para obtener \frac{899}{1562500000000000000}.

$$\frac{\frac{899}{1562500000000000000}\times 96}{\left(82\times 10^{-4}\right)^{2}}$$

Multiplica \frac{899}{1562500000000000000} y 96 para obtener \frac{2697}{48828125000000000}.

$$\frac{\frac{2697}{48828125000000000}}{\left(82\times 10^{-4}\right)^{2}}$$

Calcula 10 a la potencia de -4 y obtiene \frac{1}{10000}.

$$\frac{\frac{2697}{48828125000000000}}{\left(82\times \frac{1}{10000}\right)^{2}}$$

Multiplica 82 y \frac{1}{10000} para obtener \frac{41}{5000}.

$$\frac{\frac{2697}{48828125000000000}}{\left(\frac{41}{5000}\right)^{2}}$$

Calcula \frac{41}{5000} a la potencia de 2 y obtiene \frac{1681}{25000000}.

$$\frac{\frac{2697}{48828125000000000}}{\frac{1681}{25000000}}$$

Divide \frac{2697}{48828125000000000} por \frac{1681}{25000000} al multiplicar \frac{2697}{48828125000000000} por el recíproco de \frac{1681}{25000000}.

$$\frac{2697}{48828125000000000}\times \frac{25000000}{1681}$$

Multiplica \frac{2697}{48828125000000000} y \frac{25000000}{1681} para obtener \frac{2697}{3283203125000}.

$$\frac{2697}{3283203125000}$$

Factorizar

$$\frac{3 \cdot 29 \cdot 31}{2 ^ {3} \cdot 5 ^ {12} \cdot 41 ^ {2}} = 8,214538964901845 \times 10^{-10}$$