Solve (3.8*10^8)^3/(27.3*24*3600)^2=

$$\frac { ( 3.8 \times 10 ^ { 8 } ) ^ { 3 } } { ( 27.3 \times 24 \times 3600 ) ^ { 2 } } =$$

Evaluate

$$\frac{535859375000000000000}{54331641}\approx 9.862749682 \cdot 10^{12}$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\left(3.8\times 100000000\right)^{3}}{\left(27.3\times 24\times 3600\right)^{2}}$$

Multiply 3.8 and 100000000 to get 380000000.

$$\frac{380000000^{3}}{\left(27.3\times 24\times 3600\right)^{2}}$$

Calculate 380000000 to the power of 3 and get 54872000000000000000000000.

$$\frac{54872000000000000000000000}{\left(27.3\times 24\times 3600\right)^{2}}$$

Multiply 27.3 and 24 to get 655.2.

$$\frac{54872000000000000000000000}{\left(655.2\times 3600\right)^{2}}$$

Multiply 655.2 and 3600 to get 2358720.

$$\frac{54872000000000000000000000}{2358720^{2}}$$

Calculate 2358720 to the power of 2 and get 5563560038400.

$$\frac{54872000000000000000000000}{5563560038400}$$

Reduce the fraction \frac{54872000000000000000000000}{5563560038400} to lowest terms by extracting and canceling out 102400.

$$\frac{535859375000000000000}{54331641}$$

Factor

$$\frac{2 ^ {12} \cdot 5 ^ {19} \cdot 19 ^ {3}}{3 ^ {8} \cdot 7 ^ {2} \cdot 13 ^ {2}} = 9862749682086\frac{39320970}{54331641} = 9862749682086.725$$