Solve 1.5*10^11*(2pi/365*24*80*60)^2

$$1.5 \times 10 ^ { 11 } \times ( \frac { 2 \pi } { 365 \times 24 \times 80 \times 60 } ) ^ { 2 }$$

Evaluate

$$\frac{3125\pi ^{2}}{9208512}\approx 0.003349348$$

Solution Steps

Calculate 10 to the power of 11 and get 100000000000.

$$1.5\times 100000000000\times \left(\frac{2\pi }{365\times 24\times 80\times 60}\right)^{2}$$

Multiply 1.5 and 100000000000 to get 150000000000.

$$150000000000\times \left(\frac{2\pi }{365\times 24\times 80\times 60}\right)^{2}$$

Cancel out 2 in both numerator and denominator.

$$150000000000\times \left(\frac{\pi }{12\times 60\times 80\times 365}\right)^{2}$$

Multiply 12 and 60 to get 720.

$$150000000000\times \left(\frac{\pi }{720\times 80\times 365}\right)^{2}$$

Multiply 720 and 80 to get 57600.

$$150000000000\times \left(\frac{\pi }{57600\times 365}\right)^{2}$$

Multiply 57600 and 365 to get 21024000.

$$150000000000\times \left(\frac{\pi }{21024000}\right)^{2}$$

To raise \frac{\pi }{21024000} to a power, raise both numerator and denominator to the power and then divide.

$$150000000000\times \frac{\pi ^{2}}{21024000^{2}}$$

Express 150000000000\times \frac{\pi ^{2}}{21024000^{2}} as a single fraction.

$$\frac{150000000000\pi ^{2}}{21024000^{2}}$$

Calculate 21024000 to the power of 2 and get 442008576000000.

$$\frac{150000000000\pi ^{2}}{442008576000000}$$

Divide 150000000000\pi ^{2} by 442008576000000 to get \frac{3125}{9208512}\pi ^{2}.

$$\frac{3125}{9208512}\pi ^{2}$$

Expand

$$\frac{3125 \pi ^ {2}}{9208512} = 0.003349348271838517$$

Solution Steps

Calculate 10 to the power of 11 and get 100000000000.

$$1.5\times 100000000000\times \left(\frac{2\pi }{365\times 24\times 80\times 60}\right)^{2}$$

Multiply 1.5 and 100000000000 to get 150000000000.

$$150000000000\times \left(\frac{2\pi }{365\times 24\times 80\times 60}\right)^{2}$$

Cancel out 2 in both numerator and denominator.

$$150000000000\times \left(\frac{\pi }{12\times 60\times 80\times 365}\right)^{2}$$

Multiply 12 and 60 to get 720.

$$150000000000\times \left(\frac{\pi }{720\times 80\times 365}\right)^{2}$$

Multiply 720 and 80 to get 57600.

$$150000000000\times \left(\frac{\pi }{57600\times 365}\right)^{2}$$

Multiply 57600 and 365 to get 21024000.

$$150000000000\times \left(\frac{\pi }{21024000}\right)^{2}$$

To raise \frac{\pi }{21024000} to a power, raise both numerator and denominator to the power and then divide.

$$150000000000\times \frac{\pi ^{2}}{21024000^{2}}$$

Express 150000000000\times \frac{\pi ^{2}}{21024000^{2}} as a single fraction.

$$\frac{150000000000\pi ^{2}}{21024000^{2}}$$

Calculate 21024000 to the power of 2 and get 442008576000000.

$$\frac{150000000000\pi ^{2}}{442008576000000}$$

Divide 150000000000\pi ^{2} by 442008576000000 to get \frac{3125}{9208512}\pi ^{2}.

$$\frac{3125}{9208512}\pi ^{2}$$