Solve (6.67*10^-11)(5.98*10^24)/(6.76*10^6)^2

$$( 6.67 \times 10 ^ { - 11 } ) \frac { ( 5.98 \times 10 ^ { 24 } ) } { ( 6.76 \times 10 ^ { 6 } ) ^ { 2 } }$$

Evaluate

$$\frac{76705}{8788}\approx 8.728379609$$

Solution Steps

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

$$6.67\times \frac{1}{100000000000}\times \frac{5.98\times 10^{24}}{\left(6.76\times 10^{6}\right)^{2}}$$

Multiply 6.67 and \frac{1}{100000000000} to get \frac{667}{10000000000000}.

$$\frac{667}{10000000000000}\times \frac{5.98\times 10^{24}}{\left(6.76\times 10^{6}\right)^{2}}$$

Calculate 10 to the power of 24 and get 1000000000000000000000000.

$$\frac{667}{10000000000000}\times \frac{5.98\times 1000000000000000000000000}{\left(6.76\times 10^{6}\right)^{2}}$$

Multiply 5.98 and 1000000000000000000000000 to get 5980000000000000000000000.

$$\frac{667}{10000000000000}\times \frac{5980000000000000000000000}{\left(6.76\times 10^{6}\right)^{2}}$$

Calculate 10 to the power of 6 and get 1000000.

$$\frac{667}{10000000000000}\times \frac{5980000000000000000000000}{\left(6.76\times 1000000\right)^{2}}$$

Multiply 6.76 and 1000000 to get 6760000.

$$\frac{667}{10000000000000}\times \frac{5980000000000000000000000}{6760000^{2}}$$

Calculate 6760000 to the power of 2 and get 45697600000000.

$$\frac{667}{10000000000000}\times \frac{5980000000000000000000000}{45697600000000}$$

Reduce the fraction \frac{5980000000000000000000000}{45697600000000} to lowest terms by extracting and canceling out 20800000000.

$$\frac{667}{10000000000000}\times \frac{287500000000000}{2197}$$

Multiply \frac{667}{10000000000000} and \frac{287500000000000}{2197} to get \frac{76705}{8788}.

$$\frac{76705}{8788}$$

Factor

$$\frac{5 \cdot 29 \cdot 23 ^ {2}}{2 ^ {2} \cdot 13 ^ {3}} = 8\frac{6401}{8788} = 8.728379608557123$$