Solve 6.67*10^-11*6*10^24*(4*3600)^2/4*3.14*3.14-6.4*10^6=

$$\frac { 6.67 \times 10 ^ { - 11 } \times 6 \times 10 ^ { 24 } \times ( 4 \times 3600 ) ^ { 2 } } { 4 \times 3.14 \times 3.14 } - 6.4 \times 10 ^ { 6 } =$$

Evaluate

$$\frac{51865919999999842246400000}{24649}\approx 2.10417948 \cdot 10^{21}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 24 to get 13.

$$\frac{6.67\times 10^{13}\times 6\times \left(4\times 3600\right)^{2}}{4\times 3.14\times 3.14}-6.4\times 10^{6}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\times 6.67\times 10^{13}\times \left(4\times 3600\right)^{2}}{2\times 3.14\times 3.14}-6.4\times 10^{6}$$

Multiply 3 and 6.67 to get 20.01.

$$\frac{20.01\times 10^{13}\times \left(4\times 3600\right)^{2}}{2\times 3.14\times 3.14}-6.4\times 10^{6}$$

Calculate 10 to the power of 13 and get 10000000000000.

$$\frac{20.01\times 10000000000000\times \left(4\times 3600\right)^{2}}{2\times 3.14\times 3.14}-6.4\times 10^{6}$$

Multiply 20.01 and 10000000000000 to get 200100000000000.

$$\frac{200100000000000\times \left(4\times 3600\right)^{2}}{2\times 3.14\times 3.14}-6.4\times 10^{6}$$

Multiply 4 and 3600 to get 14400.

$$\frac{200100000000000\times 14400^{2}}{2\times 3.14\times 3.14}-6.4\times 10^{6}$$

Calculate 14400 to the power of 2 and get 207360000.

$$\frac{200100000000000\times 207360000}{2\times 3.14\times 3.14}-6.4\times 10^{6}$$

Multiply 200100000000000 and 207360000 to get 41492736000000000000000.

$$\frac{41492736000000000000000}{2\times 3.14\times 3.14}-6.4\times 10^{6}$$

Multiply 2 and 3.14 to get 6.28.

$$\frac{41492736000000000000000}{6.28\times 3.14}-6.4\times 10^{6}$$

Multiply 6.28 and 3.14 to get 19.7192.

$$\frac{41492736000000000000000}{19.7192}-6.4\times 10^{6}$$

Expand \frac{41492736000000000000000}{19.7192} by multiplying both numerator and the denominator by 10000.

$$\frac{414927360000000000000000000}{197192}-6.4\times 10^{6}$$

Reduce the fraction \frac{414927360000000000000000000}{197192} to lowest terms by extracting and canceling out 8.

$$\frac{51865920000000000000000000}{24649}-6.4\times 10^{6}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{51865920000000000000000000}{24649}-6.4\times 1000000$$

Multiply 6.4 and 1000000 to get 6400000.

$$\frac{51865920000000000000000000}{24649}-6400000$$

Subtract 6400000 from \frac{51865920000000000000000000}{24649} to get \frac{51865919999999842246400000}{24649}.

$$\frac{51865919999999842246400000}{24649}$$

Factor

$$\frac{11 \cdot 72707 \cdot 10132887042263 \cdot 2 ^ {11} \cdot 5 ^ {5}}{157 ^ {2}} = 2.104179479897758 \times 10^{21}\frac{14700}{24649} = 2.104179479897758 \times 10^{21}$$