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

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

Izračunaj

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

Koraci rješenja

Da biste pomnožili potencije s istom bazom, zbrojite eksponente. Dodajte 8 i -12 da biste dobili -4.

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

Da biste pomnožili potencije s istom bazom, zbrojite eksponente. Dodajte -4 i -16 da biste dobili -20.

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

Izračunajte koliko je -20 na 10 da biste dobili \frac{1}{100000000000000000000}.

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

Pomnožite 899 i \frac{1}{100000000000000000000} da biste dobili \frac{899}{100000000000000000000}.

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

Pomnožite \frac{899}{100000000000000000000} i 64 da biste dobili \frac{899}{1562500000000000000}.

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

Pomnožite \frac{899}{1562500000000000000} i 96 da biste dobili \frac{2697}{48828125000000000}.

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

Izračunajte koliko je -4 na 10 da biste dobili \frac{1}{10000}.

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

Pomnožite 82 i \frac{1}{10000} da biste dobili \frac{41}{5000}.

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

Izračunajte koliko je 2 na \frac{41}{5000} da biste dobili \frac{1681}{25000000}.

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

Podijelite \frac{2697}{48828125000000000} s \frac{1681}{25000000} tako da pomnožite \frac{2697}{48828125000000000} s brojem recipročnim broju \frac{1681}{25000000}.

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

Pomnožite \frac{2697}{48828125000000000} i \frac{25000000}{1681} da biste dobili \frac{2697}{3283203125000}.

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

Faktor

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