Solve 4pi^2x(15*10^9)^3/6*67*10^-11*3600*24*365

$$\frac { 4 \pi ^ { 2 } x ( 15 \times 10 ^ { 9 } ) ^ { 3 } } { 6 \cdot 67 \times 10 ^ { - 11 } \times 3600 \times 24 \times 365 }$$

Evaluate

$$\frac{1562500000000000000000000000000000000\pi ^{2}x}{14673}$$

Solution Steps

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{\pi ^{2}\times \left(15\times 10^{9}\right)^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\pi ^{2}\times \left(15\times 1000000000\right)^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Multiply 15 and 1000000000 to get 15000000000.

$$\frac{\pi ^{2}\times 15000000000^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Calculate 15000000000 to the power of 3 and get 3375000000000000000000000000000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Multiply 3 and 24 to get 72.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{72\times 67\times 365\times 1800\times 10^{-11}}$$

Multiply 72 and 67 to get 4824.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{4824\times 365\times 1800\times 10^{-11}}$$

Multiply 4824 and 365 to get 1760760.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{1760760\times 1800\times 10^{-11}}$$

Multiply 1760760 and 1800 to get 3169368000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3169368000\times 10^{-11}}$$

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

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3169368000\times \frac{1}{100000000000}}$$

Multiply 3169368000 and \frac{1}{100000000000} to get \frac{396171}{12500000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{\frac{396171}{12500000}}$$

Divide \pi ^{2}\times 3375000000000000000000000000000x by \frac{396171}{12500000} by multiplying \pi ^{2}\times 3375000000000000000000000000000x by the reciprocal of \frac{396171}{12500000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x\times 12500000}{396171}$$

Multiply 3375000000000000000000000000000 and 12500000 to get 42187500000000000000000000000000000000.

$$\frac{\pi ^{2}\times 42187500000000000000000000000000000000x}{396171}$$

Divide \pi ^{2}\times 42187500000000000000000000000000000000x by 396171 to get \pi ^{2}\times \frac{1562500000000000000000000000000000000}{14673}x.

$$\pi ^{2}\times \frac{1562500000000000000000000000000000000}{14673}x$$

Expand

$$\frac{1562500000000000000000000000000000000\pi ^{2}x}{14673}$$

Solution Steps

Cancel out 2\times 2 in both numerator and denominator.

$$\frac{\pi ^{2}\times \left(15\times 10^{9}\right)^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$\frac{\pi ^{2}\times \left(15\times 1000000000\right)^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Multiply 15 and 1000000000 to get 15000000000.

$$\frac{\pi ^{2}\times 15000000000^{3}x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Calculate 15000000000 to the power of 3 and get 3375000000000000000000000000000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3\times 24\times 67\times 365\times 1800\times 10^{-11}}$$

Multiply 3 and 24 to get 72.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{72\times 67\times 365\times 1800\times 10^{-11}}$$

Multiply 72 and 67 to get 4824.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{4824\times 365\times 1800\times 10^{-11}}$$

Multiply 4824 and 365 to get 1760760.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{1760760\times 1800\times 10^{-11}}$$

Multiply 1760760 and 1800 to get 3169368000.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3169368000\times 10^{-11}}$$

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

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{3169368000\times \frac{1}{100000000000}}$$

Multiply 3169368000 and \frac{1}{100000000000} to get \frac{396171}{12500000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x}{\frac{396171}{12500000}}$$

Divide \pi ^{2}\times 3375000000000000000000000000000x by \frac{396171}{12500000} by multiplying \pi ^{2}\times 3375000000000000000000000000000x by the reciprocal of \frac{396171}{12500000}.

$$\frac{\pi ^{2}\times 3375000000000000000000000000000x\times 12500000}{396171}$$

Multiply 3375000000000000000000000000000 and 12500000 to get 42187500000000000000000000000000000000.

$$\frac{\pi ^{2}\times 42187500000000000000000000000000000000x}{396171}$$

Divide \pi ^{2}\times 42187500000000000000000000000000000000x by 396171 to get \pi ^{2}\times \frac{1562500000000000000000000000000000000}{14673}x.

$$\pi ^{2}\times \frac{1562500000000000000000000000000000000}{14673}x$$