Solve frac{4(3.14)^{2}*(1.5*10^{11})^3}{6.82*10^-11*(3.2*10^7)^2}

$$\frac { 4 ( 3.14 ) ^ { 2 } \times ( 1.5 \times 10 ^ { 11 } ) ^ { 3 } } { 6.82 \times 10 ^ { - 11 } \times ( 3.2 \times 10 ^ { 7 } ) ^ { 2 } }$$

Evaluate

$$\frac{649924804687500000000000000000000}{341}\approx 1.905937844 \cdot 10^{30}$$

Solution Steps

Calculate 3.14 to the power of 2 and get 9.8596.

$$\frac{4\times 9.8596\times \left(1.5\times 10^{11}\right)^{3}}{6.82\times 10^{-11}\times \left(3.2\times 10^{7}\right)^{2}}$$

Multiply 4 and 9.8596 to get 39.4384.

$$\frac{39.4384\times \left(1.5\times 10^{11}\right)^{3}}{6.82\times 10^{-11}\times \left(3.2\times 10^{7}\right)^{2}}$$

Calculate 10 to the power of 11 and get 100000000000.

$$\frac{39.4384\times \left(1.5\times 100000000000\right)^{3}}{6.82\times 10^{-11}\times \left(3.2\times 10^{7}\right)^{2}}$$

Multiply 1.5 and 100000000000 to get 150000000000.

$$\frac{39.4384\times 150000000000^{3}}{6.82\times 10^{-11}\times \left(3.2\times 10^{7}\right)^{2}}$$

Calculate 150000000000 to the power of 3 and get 3375000000000000000000000000000000.

$$\frac{39.4384\times 3375000000000000000000000000000000}{6.82\times 10^{-11}\times \left(3.2\times 10^{7}\right)^{2}}$$

Multiply 39.4384 and 3375000000000000000000000000000000 to get 133104600000000000000000000000000000.

$$\frac{133104600000000000000000000000000000}{6.82\times 10^{-11}\times \left(3.2\times 10^{7}\right)^{2}}$$

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

$$\frac{133104600000000000000000000000000000}{6.82\times \frac{1}{100000000000}\times \left(3.2\times 10^{7}\right)^{2}}$$

Multiply 6.82 and \frac{1}{100000000000} to get \frac{341}{5000000000000}.

$$\frac{133104600000000000000000000000000000}{\frac{341}{5000000000000}\times \left(3.2\times 10^{7}\right)^{2}}$$

Calculate 10 to the power of 7 and get 10000000.

$$\frac{133104600000000000000000000000000000}{\frac{341}{5000000000000}\times \left(3.2\times 10000000\right)^{2}}$$

Multiply 3.2 and 10000000 to get 32000000.

$$\frac{133104600000000000000000000000000000}{\frac{341}{5000000000000}\times 32000000^{2}}$$

Calculate 32000000 to the power of 2 and get 1024000000000000.

$$\frac{133104600000000000000000000000000000}{\frac{341}{5000000000000}\times 1024000000000000}$$

Multiply \frac{341}{5000000000000} and 1024000000000000 to get \frac{349184}{5}.

$$\frac{133104600000000000000000000000000000}{\frac{349184}{5}}$$

Divide 133104600000000000000000000000000000 by \frac{349184}{5} by multiplying 133104600000000000000000000000000000 by the reciprocal of \frac{349184}{5}.

$$133104600000000000000000000000000000\times \frac{5}{349184}$$

Multiply 133104600000000000000000000000000000 and \frac{5}{349184} to get \frac{649924804687500000000000000000000}{341}.

$$\frac{649924804687500000000000000000000}{341}$$

Factor

$$\frac{2 ^ {20} \cdot 3 ^ {3} \cdot 5 ^ {30} \cdot 157 ^ {2}}{11 \cdot 31} = 1.905937843658358 \times 10^{30}\frac{216}{341} = 1.905937843658358 \times 10^{30}$$