Solve 8.9910^86.410^-129.610^-16/{left(8.210^-4right)^2}

$$\frac{ 8.99 { 10 }^{ 8 } 6.4 { 10 }^{ -12 } 9.6 { 10 }^{ -16 } }{ { \left(8.2 { 10 }^{ -4 } \right) }^{ 2 } }$$

Evaluate

$$\frac{2697}{328320312500000}\approx 8.214538965 \cdot 10^{-12}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 8 and -12 to get -4.

$$\frac{8.99\times 10^{-4}\times 6.4\times 9.6\times 10^{-16}}{\left(8.2\times 10^{-4}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add -4 and -16 to get -20.

$$\frac{8.99\times 10^{-20}\times 6.4\times 9.6}{\left(8.2\times 10^{-4}\right)^{2}}$$

Calculate 10 to the power of -20 and get \frac{1}{100000000000000000000}.

$$\frac{8.99\times \frac{1}{100000000000000000000}\times 6.4\times 9.6}{\left(8.2\times 10^{-4}\right)^{2}}$$

Multiply 8.99 and \frac{1}{100000000000000000000} to get \frac{899}{10000000000000000000000}.

$$\frac{\frac{899}{10000000000000000000000}\times 6.4\times 9.6}{\left(8.2\times 10^{-4}\right)^{2}}$$

Multiply \frac{899}{10000000000000000000000} and 6.4 to get \frac{899}{1562500000000000000000}.

$$\frac{\frac{899}{1562500000000000000000}\times 9.6}{\left(8.2\times 10^{-4}\right)^{2}}$$

Multiply \frac{899}{1562500000000000000000} and 9.6 to get \frac{2697}{488281250000000000000}.

$$\frac{\frac{2697}{488281250000000000000}}{\left(8.2\times 10^{-4}\right)^{2}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{\frac{2697}{488281250000000000000}}{\left(8.2\times \frac{1}{10000}\right)^{2}}$$

Multiply 8.2 and \frac{1}{10000} to get \frac{41}{50000}.

$$\frac{\frac{2697}{488281250000000000000}}{\left(\frac{41}{50000}\right)^{2}}$$

Calculate \frac{41}{50000} to the power of 2 and get \frac{1681}{2500000000}.

$$\frac{\frac{2697}{488281250000000000000}}{\frac{1681}{2500000000}}$$

Divide \frac{2697}{488281250000000000000} by \frac{1681}{2500000000} by multiplying \frac{2697}{488281250000000000000} by the reciprocal of \frac{1681}{2500000000}.

$$\frac{2697}{488281250000000000000}\times \frac{2500000000}{1681}$$

Multiply \frac{2697}{488281250000000000000} and \frac{2500000000}{1681} to get \frac{2697}{328320312500000}.

$$\frac{2697}{328320312500000}$$

Factor

$$\frac{3 \cdot 29 \cdot 31}{2 ^ {5} \cdot 5 ^ {14} \cdot 41 ^ {2}} = 8.214538964901845 \times 10^{-12}$$