Solve 2pi*10*8.85*10^-125*10^-2/ln(frac{e*8*10^-3{8*10^-3})}

$$2 \pi \times 10 \times 8.85 \times { 10 }^{ -12 } \frac{ 5 \times { 10 }^{ -2 } }{ \ln ( \frac{ e \times 8 \times { 10 }^{ -3 } }{ 8 \times { 10 }^{ -3 } } ) }$$

Evaluate

$$\frac{177\pi }{20000000000000}\approx 2.780309498 \cdot 10^{-11}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and -12 to get -11.

$$2\pi \times 10^{-11}\times 8.85\times \frac{5\times 10^{-2}}{\log_{e}\left(\frac{e\times 8\times 10^{-3}}{8\times 10^{-3}}\right)}$$

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

$$2\pi \times \frac{1}{100000000000}\times 8.85\times \frac{5\times 10^{-2}}{\log_{e}\left(\frac{e\times 8\times 10^{-3}}{8\times 10^{-3}}\right)}$$

Multiply 2 and \frac{1}{100000000000} to get \frac{1}{50000000000}.

$$\frac{1}{50000000000}\pi \times 8.85\times \frac{5\times 10^{-2}}{\log_{e}\left(\frac{e\times 8\times 10^{-3}}{8\times 10^{-3}}\right)}$$

Multiply \frac{1}{50000000000} and 8.85 to get \frac{177}{1000000000000}.

$$\frac{177}{1000000000000}\pi \times \frac{5\times 10^{-2}}{\log_{e}\left(\frac{e\times 8\times 10^{-3}}{8\times 10^{-3}}\right)}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{177}{1000000000000}\pi \times \frac{5\times \frac{1}{100}}{\log_{e}\left(\frac{e\times 8\times 10^{-3}}{8\times 10^{-3}}\right)}$$

Multiply 5 and \frac{1}{100} to get \frac{1}{20}.

$$\frac{177}{1000000000000}\pi \times \frac{\frac{1}{20}}{\log_{e}\left(\frac{e\times 8\times 10^{-3}}{8\times 10^{-3}}\right)}$$

Cancel out 8\times 10^{-3} in both numerator and denominator.

$$\frac{177}{1000000000000}\pi \times \frac{\frac{1}{20}}{\log_{e}\left(e\right)}$$

The base e logarithm of e is 1.

$$\frac{177}{1000000000000}\pi \times \frac{\frac{1}{20}}{1}$$

Anything divided by one gives itself.

$$\frac{177}{1000000000000}\pi \times \frac{1}{20}$$

Multiply \frac{177}{1000000000000} and \frac{1}{20} to get \frac{177}{20000000000000}.

$$\frac{177}{20000000000000}\pi$$