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

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

Avaliar

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

Passos Para a Resolução

Para multiplicar as potências da mesma base, some os seus expoentes. Some 8 e -12 para obter -4.

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

Para multiplicar as potências da mesma base, some os seus expoentes. Some -4 e -16 para obter -20.

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

Calcule 10 elevado a -20 e obtenha \frac{1}{100000000000000000000}.

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

Multiplique 899 e \frac{1}{100000000000000000000} para obter \frac{899}{100000000000000000000}.

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

Multiplique \frac{899}{100000000000000000000} e 64 para obter \frac{899}{1562500000000000000}.

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

Multiplique \frac{899}{1562500000000000000} e 96 para obter \frac{2697}{48828125000000000}.

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

Calcule 10 elevado a -4 e obtenha \frac{1}{10000}.

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

Multiplique 82 e \frac{1}{10000} para obter \frac{41}{5000}.

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

Calcule \frac{41}{5000} elevado a 2 e obtenha \frac{1681}{25000000}.

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

Divida \frac{2697}{48828125000000000} por \frac{1681}{25000000} ao multiplicar \frac{2697}{48828125000000000} pelo recíproco de \frac{1681}{25000000}.

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

Multiplique \frac{2697}{48828125000000000} e \frac{25000000}{1681} para obter \frac{2697}{3283203125000}.

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

Fatorizar

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