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

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

Evaluate

$$9.7705078125$$

Solution Steps

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

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

Calculate 10 to the power of 13 and get 10000000000000.

$$\frac{6.67\times 10000000000000\times 6}{\left(6.4\times 10^{6}\right)^{2}}$$

Multiply 6.67 and 10000000000000 to get 66700000000000.

$$\frac{66700000000000\times 6}{\left(6.4\times 10^{6}\right)^{2}}$$

Multiply 66700000000000 and 6 to get 400200000000000.

$$\frac{400200000000000}{\left(6.4\times 10^{6}\right)^{2}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{400200000000000}{\left(6.4\times 1000000\right)^{2}}$$

Multiply 6.4 and 1000000 to get 6400000.

$$\frac{400200000000000}{6400000^{2}}$$

Calculate 6400000 to the power of 2 and get 40960000000000.

$$\frac{400200000000000}{40960000000000}$$

Reduce the fraction \frac{400200000000000}{40960000000000} to lowest terms by extracting and canceling out 40000000000.

$$\frac{10005}{1024}$$

Factor

$$\frac{3 \cdot 5 \cdot 23 \cdot 29}{2 ^ {10}} = 9\frac{789}{1024} = 9.7705078125$$