Solve frac{6*10^{3}*45*10^-3}{pi/32*(100*10^-3)^4[1-(80/100)^4]}

$$\frac { 6 \times 10 ^ { 3 } \times 45 \times 10 ^ { - 3 } } { \frac { \pi } { 32 } \cdot ( 100 \times 10 ^ { - 3 } ) ^ { 4 } [ 1 - ( \frac { 80 } { 100 } ) ^ { 4 } ] }$$

Evaluate

$$\frac{6000000000}{41\pi }\approx 46581934.563481569$$

Solution Steps

Multiply 10^{3} and 10^{-3} to get 1.

$$\frac{6\times 45}{\frac{\pi }{32}\times \left(100\times 10^{-3}\right)^{4}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

Multiply 6 and 45 to get 270.

$$\frac{270}{\frac{\pi }{32}\times \left(100\times 10^{-3}\right)^{4}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{270}{\frac{\pi }{32}\times \left(100\times \frac{1}{1000}\right)^{4}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

Multiply 100 and \frac{1}{1000} to get \frac{1}{10}.

$$\frac{270}{\frac{\pi }{32}\times \left(\frac{1}{10}\right)^{4}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

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

$$\frac{270}{\frac{\pi }{32}\times \frac{1}{10000}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$\frac{270}{\frac{\pi }{32}\times \frac{1}{10000}\left(1-\left(\frac{4}{5}\right)^{4}\right)}$$

Calculate \frac{4}{5} to the power of 4 and get \frac{256}{625}.

$$\frac{270}{\frac{\pi }{32}\times \frac{1}{10000}\left(1-\frac{256}{625}\right)}$$

Subtract \frac{256}{625} from 1 to get \frac{369}{625}.

$$\frac{270}{\frac{\pi }{32}\times \frac{1}{10000}\times \frac{369}{625}}$$

Multiply \frac{1}{10000} and \frac{369}{625} to get \frac{369}{6250000}.

$$\frac{270}{\frac{\pi }{32}\times \frac{369}{6250000}}$$

Multiply \frac{\pi }{32} times \frac{369}{6250000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{270}{\frac{\pi \times 369}{32\times 6250000}}$$

Divide 270 by \frac{\pi \times 369}{32\times 6250000} by multiplying 270 by the reciprocal of \frac{\pi \times 369}{32\times 6250000}.

$$\frac{270\times 32\times 6250000}{\pi \times 369}$$

Cancel out 9 in both numerator and denominator.

$$\frac{30\times 32\times 6250000}{41\pi }$$

Multiply 30 and 32 to get 960.

$$\frac{960\times 6250000}{41\pi }$$

Multiply 960 and 6250000 to get 6000000000.

$$\frac{6000000000}{41\pi }$$

Expand

$$\frac{6000000000}{41 \pi} = 46581934.56348157$$

Solution Steps

Multiply 10^{3} and 10^{-3} to get 1.

$$\frac{6\times 45}{\frac{\pi }{32}\times \left(100\times 10^{-3}\right)^{4}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

Multiply 6 and 45 to get 270.

$$\frac{270}{\frac{\pi }{32}\times \left(100\times 10^{-3}\right)^{4}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

Calculate 10 to the power of -3 and get \frac{1}{1000}.

$$\frac{270}{\frac{\pi }{32}\times \left(100\times \frac{1}{1000}\right)^{4}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

Multiply 100 and \frac{1}{1000} to get \frac{1}{10}.

$$\frac{270}{\frac{\pi }{32}\times \left(\frac{1}{10}\right)^{4}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

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

$$\frac{270}{\frac{\pi }{32}\times \frac{1}{10000}\left(1-\left(\frac{80}{100}\right)^{4}\right)}$$

Reduce the fraction \frac{80}{100} to lowest terms by extracting and canceling out 20.

$$\frac{270}{\frac{\pi }{32}\times \frac{1}{10000}\left(1-\left(\frac{4}{5}\right)^{4}\right)}$$

Calculate \frac{4}{5} to the power of 4 and get \frac{256}{625}.

$$\frac{270}{\frac{\pi }{32}\times \frac{1}{10000}\left(1-\frac{256}{625}\right)}$$

Subtract \frac{256}{625} from 1 to get \frac{369}{625}.

$$\frac{270}{\frac{\pi }{32}\times \frac{1}{10000}\times \frac{369}{625}}$$

Multiply \frac{1}{10000} and \frac{369}{625} to get \frac{369}{6250000}.

$$\frac{270}{\frac{\pi }{32}\times \frac{369}{6250000}}$$

Multiply \frac{\pi }{32} times \frac{369}{6250000} by multiplying numerator times numerator and denominator times denominator.

$$\frac{270}{\frac{\pi \times 369}{32\times 6250000}}$$

Divide 270 by \frac{\pi \times 369}{32\times 6250000} by multiplying 270 by the reciprocal of \frac{\pi \times 369}{32\times 6250000}.

$$\frac{270\times 32\times 6250000}{\pi \times 369}$$

Cancel out 9 in both numerator and denominator.

$$\frac{30\times 32\times 6250000}{41\pi }$$

Multiply 30 and 32 to get 960.

$$\frac{960\times 6250000}{41\pi }$$

Multiply 960 and 6250000 to get 6000000000.

$$\frac{6000000000}{41\pi }$$