Solve frac{(3.84*10^{8})^{3}*4*pi^2}{(2.36*10^6)^2*6.67*10^-11}

$$\frac { ( 3.84 \times 10 ^ { 8 } ) ^ { 3 } \times 4 \times \pi ^ { 2 } } { ( 2.36 \times 10 ^ { 6 } ) ^ { 2 } \times 6.67 \times 10 ^ { - 11 } }$$

Evaluate

$$\frac{1415577600000000000000000000000\pi ^{2}}{2321827}\approx 6.017326403 \cdot 10^{24}$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\left(3.84\times 100000000\right)^{3}\times 4\pi ^{2}}{\left(2.36\times 10^{6}\right)^{2}\times 6.67\times 10^{-11}}$$

Multiply 3.84 and 100000000 to get 384000000.

$$\frac{384000000^{3}\times 4\pi ^{2}}{\left(2.36\times 10^{6}\right)^{2}\times 6.67\times 10^{-11}}$$

Calculate 384000000 to the power of 3 and get 56623104000000000000000000.

$$\frac{56623104000000000000000000\times 4\pi ^{2}}{\left(2.36\times 10^{6}\right)^{2}\times 6.67\times 10^{-11}}$$

Multiply 56623104000000000000000000 and 4 to get 226492416000000000000000000.

$$\frac{226492416000000000000000000\pi ^{2}}{\left(2.36\times 10^{6}\right)^{2}\times 6.67\times 10^{-11}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{226492416000000000000000000\pi ^{2}}{\left(2.36\times 1000000\right)^{2}\times 6.67\times 10^{-11}}$$

Multiply 2.36 and 1000000 to get 2360000.

$$\frac{226492416000000000000000000\pi ^{2}}{2360000^{2}\times 6.67\times 10^{-11}}$$

Calculate 2360000 to the power of 2 and get 5569600000000.

$$\frac{226492416000000000000000000\pi ^{2}}{5569600000000\times 6.67\times 10^{-11}}$$

Multiply 5569600000000 and 6.67 to get 37149232000000.

$$\frac{226492416000000000000000000\pi ^{2}}{37149232000000\times 10^{-11}}$$

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

$$\frac{226492416000000000000000000\pi ^{2}}{37149232000000\times \frac{1}{100000000000}}$$

Multiply 37149232000000 and \frac{1}{100000000000} to get \frac{2321827}{6250}.

$$\frac{226492416000000000000000000\pi ^{2}}{\frac{2321827}{6250}}$$

Divide 226492416000000000000000000\pi ^{2} by \frac{2321827}{6250} by multiplying 226492416000000000000000000\pi ^{2} by the reciprocal of \frac{2321827}{6250}.

$$\frac{226492416000000000000000000\pi ^{2}\times 6250}{2321827}$$

Multiply 226492416000000000000000000 and 6250 to get 1415577600000000000000000000000.

$$\frac{1415577600000000000000000000000\pi ^{2}}{2321827}$$

Expand

$$\frac{1415577600000000000000000000000 \pi ^ {2}}{2321827} = 6.017326403320967 \times 10^{24}\frac{64500}{2321827} = 6.017326403320967 \times 10^{24}$$

Solution Steps

Calculate 10 to the power of 8 and get 100000000.

$$\frac{\left(3.84\times 100000000\right)^{3}\times 4\pi ^{2}}{\left(2.36\times 10^{6}\right)^{2}\times 6.67\times 10^{-11}}$$

Multiply 3.84 and 100000000 to get 384000000.

$$\frac{384000000^{3}\times 4\pi ^{2}}{\left(2.36\times 10^{6}\right)^{2}\times 6.67\times 10^{-11}}$$

Calculate 384000000 to the power of 3 and get 56623104000000000000000000.

$$\frac{56623104000000000000000000\times 4\pi ^{2}}{\left(2.36\times 10^{6}\right)^{2}\times 6.67\times 10^{-11}}$$

Multiply 56623104000000000000000000 and 4 to get 226492416000000000000000000.

$$\frac{226492416000000000000000000\pi ^{2}}{\left(2.36\times 10^{6}\right)^{2}\times 6.67\times 10^{-11}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{226492416000000000000000000\pi ^{2}}{\left(2.36\times 1000000\right)^{2}\times 6.67\times 10^{-11}}$$

Multiply 2.36 and 1000000 to get 2360000.

$$\frac{226492416000000000000000000\pi ^{2}}{2360000^{2}\times 6.67\times 10^{-11}}$$

Calculate 2360000 to the power of 2 and get 5569600000000.

$$\frac{226492416000000000000000000\pi ^{2}}{5569600000000\times 6.67\times 10^{-11}}$$

Multiply 5569600000000 and 6.67 to get 37149232000000.

$$\frac{226492416000000000000000000\pi ^{2}}{37149232000000\times 10^{-11}}$$

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

$$\frac{226492416000000000000000000\pi ^{2}}{37149232000000\times \frac{1}{100000000000}}$$

Multiply 37149232000000 and \frac{1}{100000000000} to get \frac{2321827}{6250}.

$$\frac{226492416000000000000000000\pi ^{2}}{\frac{2321827}{6250}}$$

Divide 226492416000000000000000000\pi ^{2} by \frac{2321827}{6250} by multiplying 226492416000000000000000000\pi ^{2} by the reciprocal of \frac{2321827}{6250}.

$$\frac{226492416000000000000000000\pi ^{2}\times 6250}{2321827}$$

Multiply 226492416000000000000000000 and 6250 to get 1415577600000000000000000000000.

$$\frac{1415577600000000000000000000000\pi ^{2}}{2321827}$$