Solve 4pi^2*(1.5*10^9)^3/365*24*3600*6.67*10^-11

$$\frac { 4 \pi ^ { 2 } \cdot ( 1.5 \times 10 ^ { 9 } ) ^ { 3 } } { 365 \times 24 \times 3600 \times 6.67 \times 10 ^ { - 11 } }$$

Evaluate

$$\frac{312500000000000000000000000000000000\pi ^{2}}{48691}\approx 6.334335658 \cdot 10^{31}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{\pi ^{2}\times \left(1.5\times 10^{9}\right)^{3}}{6\times 6.67\times 365\times 3600\times 10^{-11}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\pi ^{2}\times \left(1.5\times 1000000000\right)^{3}}{6\times 6.67\times 365\times 3600\times 10^{-11}}$$

Multiply 1.5 and 1000000000 to get 1500000000.

$$\frac{\pi ^{2}\times 1500000000^{3}}{6\times 6.67\times 365\times 3600\times 10^{-11}}$$

Calculate 1500000000 to the power of 3 and get 3375000000000000000000000000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{6\times 6.67\times 365\times 3600\times 10^{-11}}$$

Multiply 6 and 6.67 to get 40.02.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{40.02\times 365\times 3600\times 10^{-11}}$$

Multiply 40.02 and 365 to get 14607.3.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{14607.3\times 3600\times 10^{-11}}$$

Multiply 14607.3 and 3600 to get 52586280.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{52586280\times 10^{-11}}$$

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

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{52586280\times \frac{1}{100000000000}}$$

Multiply 52586280 and \frac{1}{100000000000} to get \frac{1314657}{2500000000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{\frac{1314657}{2500000000}}$$

Divide \pi ^{2}\times 3375000000000000000000000000 by \frac{1314657}{2500000000} by multiplying \pi ^{2}\times 3375000000000000000000000000 by the reciprocal of \frac{1314657}{2500000000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000\times 2500000000}{1314657}$$

Multiply 3375000000000000000000000000 and 2500000000 to get 8437500000000000000000000000000000000.

$$\frac{\pi ^{2}\times 8437500000000000000000000000000000000}{1314657}$$

Divide \pi ^{2}\times 8437500000000000000000000000000000000 by 1314657 to get \pi ^{2}\times \frac{312500000000000000000000000000000000}{48691}.

$$\pi ^{2}\times \frac{312500000000000000000000000000000000}{48691}$$

Expand

$$\frac{312500000000000000000000000000000000 \pi ^ {2}}{48691} = 6.334335658212862 \times 10^{31}\frac{22902}{48691} = 6.334335658212862 \times 10^{31}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\frac{\pi ^{2}\times \left(1.5\times 10^{9}\right)^{3}}{6\times 6.67\times 365\times 3600\times 10^{-11}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\pi ^{2}\times \left(1.5\times 1000000000\right)^{3}}{6\times 6.67\times 365\times 3600\times 10^{-11}}$$

Multiply 1.5 and 1000000000 to get 1500000000.

$$\frac{\pi ^{2}\times 1500000000^{3}}{6\times 6.67\times 365\times 3600\times 10^{-11}}$$

Calculate 1500000000 to the power of 3 and get 3375000000000000000000000000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{6\times 6.67\times 365\times 3600\times 10^{-11}}$$

Multiply 6 and 6.67 to get 40.02.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{40.02\times 365\times 3600\times 10^{-11}}$$

Multiply 40.02 and 365 to get 14607.3.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{14607.3\times 3600\times 10^{-11}}$$

Multiply 14607.3 and 3600 to get 52586280.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{52586280\times 10^{-11}}$$

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

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{52586280\times \frac{1}{100000000000}}$$

Multiply 52586280 and \frac{1}{100000000000} to get \frac{1314657}{2500000000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000}{\frac{1314657}{2500000000}}$$

Divide \pi ^{2}\times 3375000000000000000000000000 by \frac{1314657}{2500000000} by multiplying \pi ^{2}\times 3375000000000000000000000000 by the reciprocal of \frac{1314657}{2500000000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000\times 2500000000}{1314657}$$

Multiply 3375000000000000000000000000 and 2500000000 to get 8437500000000000000000000000000000000.

$$\frac{\pi ^{2}\times 8437500000000000000000000000000000000}{1314657}$$

Divide \pi ^{2}\times 8437500000000000000000000000000000000 by 1314657 to get \pi ^{2}\times \frac{312500000000000000000000000000000000}{48691}.

$$\pi ^{2}\times \frac{312500000000000000000000000000000000}{48691}$$