Solve 4*3.14^2left(1.5*10^11right)^3/6.672*10^-11{left(365*24*3600right)^2}

$$\frac{ 4 \times { 3.14 }^{ 2 } { \left(1.5 \times { 10 }^{ 11 } \right) }^{ 3 } }{ 6.672 \times { 10 }^{ -11 } { \left(365 \times 24 \times 3600 \right) }^{ 2 } }$$

Evaluate

$$\frac{120356445312500000000000000000000000000}{59999211}\approx 2.005967134 \cdot 10^{30}$$

Solution Steps

Calculate 3.14 to the power of 2 and get 9.8596.

$$\frac{4\times 9.8596\times \left(1.5\times 10^{11}\right)^{3}}{6.672\times 10^{-11}\times \left(365\times 24\times 3600\right)^{2}}$$

Multiply 4 and 9.8596 to get 39.4384.

$$\frac{39.4384\times \left(1.5\times 10^{11}\right)^{3}}{6.672\times 10^{-11}\times \left(365\times 24\times 3600\right)^{2}}$$

Calculate 10 to the power of 11 and get 100000000000.

$$\frac{39.4384\times \left(1.5\times 100000000000\right)^{3}}{6.672\times 10^{-11}\times \left(365\times 24\times 3600\right)^{2}}$$

Multiply 1.5 and 100000000000 to get 150000000000.

$$\frac{39.4384\times 150000000000^{3}}{6.672\times 10^{-11}\times \left(365\times 24\times 3600\right)^{2}}$$

Calculate 150000000000 to the power of 3 and get 3375000000000000000000000000000000.

$$\frac{39.4384\times 3375000000000000000000000000000000}{6.672\times 10^{-11}\times \left(365\times 24\times 3600\right)^{2}}$$

Multiply 39.4384 and 3375000000000000000000000000000000 to get 133104600000000000000000000000000000.

$$\frac{133104600000000000000000000000000000}{6.672\times 10^{-11}\times \left(365\times 24\times 3600\right)^{2}}$$

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

$$\frac{133104600000000000000000000000000000}{6.672\times \frac{1}{100000000000}\times \left(365\times 24\times 3600\right)^{2}}$$

Multiply 6.672 and \frac{1}{100000000000} to get \frac{417}{6250000000000}.

$$\frac{133104600000000000000000000000000000}{\frac{417}{6250000000000}\times \left(365\times 24\times 3600\right)^{2}}$$

Multiply 365 and 24 to get 8760.

$$\frac{133104600000000000000000000000000000}{\frac{417}{6250000000000}\times \left(8760\times 3600\right)^{2}}$$

Multiply 8760 and 3600 to get 31536000.

$$\frac{133104600000000000000000000000000000}{\frac{417}{6250000000000}\times 31536000^{2}}$$

Calculate 31536000 to the power of 2 and get 994519296000000.

$$\frac{133104600000000000000000000000000000}{\frac{417}{6250000000000}\times 994519296000000}$$

Multiply \frac{417}{6250000000000} and 994519296000000 to get \frac{25919659152}{390625}.

$$\frac{133104600000000000000000000000000000}{\frac{25919659152}{390625}}$$

Divide 133104600000000000000000000000000000 by \frac{25919659152}{390625} by multiplying 133104600000000000000000000000000000 by the reciprocal of \frac{25919659152}{390625}.

$$133104600000000000000000000000000000\times \frac{390625}{25919659152}$$

Multiply 133104600000000000000000000000000000 and \frac{390625}{25919659152} to get \frac{120356445312500000000000000000000000000}{59999211}.

$$\frac{120356445312500000000000000000000000000}{59999211}$$

Factor

$$\frac{2 ^ {26} \cdot 5 ^ {37} \cdot 157 ^ {2}}{139 \cdot 3 ^ {4} \cdot 73 ^ {2}} = 2.005967133676141 \times 10^{30}\frac{8069629}{59999211} = 2.005967133676141 \times 10^{30}$$