Solve 4/3*left(1.64*10^-6right)^3*0.851*10^3div1.92div10^5div1.6div{10}^-19

$$\frac{ 4 }{ 3 } \times { \left(1.64 \times { 10 }^{ -6 } \right) }^{ 3 } \times 0.851 \times { 10 }^{ 3 } \div 1.92 \div { 10 }^{ 5 } \div 1.6 \div { 10 }^{ -19 }$$

Evaluate

$$\frac{58651771}{360000000}\approx 0.162921586$$

Solution Steps

Express \frac{\frac{\frac{\frac{4}{3}\times \left(1.64\times 10^{-6}\right)^{3}\times 0.851\times 10^{3}}{1.92}}{10^{5}}}{1.6} as a single fraction.

$$\frac{\frac{\frac{\frac{4}{3}\times \left(1.64\times 10^{-6}\right)^{3}\times 0.851\times 10^{3}}{1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Calculate 10 to the power of -6 and get \frac{1}{1000000}.

$$\frac{\frac{\frac{\frac{4}{3}\times \left(1.64\times \frac{1}{1000000}\right)^{3}\times 0.851\times 10^{3}}{1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Multiply 1.64 and \frac{1}{1000000} to get \frac{41}{25000000}.

$$\frac{\frac{\frac{\frac{4}{3}\times \left(\frac{41}{25000000}\right)^{3}\times 0.851\times 10^{3}}{1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Calculate \frac{41}{25000000} to the power of 3 and get \frac{68921}{15625000000000000000000}.

$$\frac{\frac{\frac{\frac{4}{3}\times \frac{68921}{15625000000000000000000}\times 0.851\times 10^{3}}{1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Multiply \frac{4}{3} and \frac{68921}{15625000000000000000000} to get \frac{68921}{11718750000000000000000}.

$$\frac{\frac{\frac{\frac{68921}{11718750000000000000000}\times 0.851\times 10^{3}}{1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Multiply \frac{68921}{11718750000000000000000} and 0.851 to get \frac{58651771}{11718750000000000000000000}.

$$\frac{\frac{\frac{\frac{58651771}{11718750000000000000000000}\times 10^{3}}{1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Calculate 10 to the power of 3 and get 1000.

$$\frac{\frac{\frac{\frac{58651771}{11718750000000000000000000}\times 1000}{1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Multiply \frac{58651771}{11718750000000000000000000} and 1000 to get \frac{58651771}{11718750000000000000000}.

$$\frac{\frac{\frac{\frac{58651771}{11718750000000000000000}}{1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Express \frac{\frac{58651771}{11718750000000000000000}}{1.92} as a single fraction.

$$\frac{\frac{\frac{58651771}{11718750000000000000000\times 1.92}}{10^{5}\times 1.6}}{10^{-19}}$$

Multiply 11718750000000000000000 and 1.92 to get 22500000000000000000000.

$$\frac{\frac{\frac{58651771}{22500000000000000000000}}{10^{5}\times 1.6}}{10^{-19}}$$

Calculate 10 to the power of 5 and get 100000.

$$\frac{\frac{\frac{58651771}{22500000000000000000000}}{100000\times 1.6}}{10^{-19}}$$

Multiply 100000 and 1.6 to get 160000.

$$\frac{\frac{\frac{58651771}{22500000000000000000000}}{160000}}{10^{-19}}$$

Express \frac{\frac{58651771}{22500000000000000000000}}{160000} as a single fraction.

$$\frac{\frac{58651771}{22500000000000000000000\times 160000}}{10^{-19}}$$

Multiply 22500000000000000000000 and 160000 to get 3600000000000000000000000000.

$$\frac{\frac{58651771}{3600000000000000000000000000}}{10^{-19}}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\frac{\frac{58651771}{3600000000000000000000000000}}{\frac{1}{10000000000000000000}}$$

Divide \frac{58651771}{3600000000000000000000000000} by \frac{1}{10000000000000000000} by multiplying \frac{58651771}{3600000000000000000000000000} by the reciprocal of \frac{1}{10000000000000000000}.

$$\frac{58651771}{3600000000000000000000000000}\times 10000000000000000000$$

Multiply \frac{58651771}{3600000000000000000000000000} and 10000000000000000000 to get \frac{58651771}{360000000}.

$$\frac{58651771}{360000000}$$

Factor

$$\frac{23 \cdot 37 \cdot 41 ^ {3}}{2 ^ {9} \cdot 3 ^ {2} \cdot 5 ^ {7}} = 0.1629215861111111$$