Solve 6.67+10^-11*1.989*10^30/(148.54*10^9)^2

$$6.67 + 10 ^ { - 11 } \cdot 1.989 * 10 ^ { 30 } / ( 148.54 * 10 ^ { 9 } ) ^ { 2 }$$

Evaluate

$$\frac{36796911943}{5516032900}\approx 6.670901463$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and 30 to get 19.

$$6.67+\frac{10^{19}\times 1.989}{\left(148.54\times 10^{9}\right)^{2}}$$

Calculate 10 to the power of 19 and get 10000000000000000000.

$$6.67+\frac{10000000000000000000\times 1.989}{\left(148.54\times 10^{9}\right)^{2}}$$

Multiply 10000000000000000000 and 1.989 to get 19890000000000000000.

$$6.67+\frac{19890000000000000000}{\left(148.54\times 10^{9}\right)^{2}}$$

Calculate 10 to the power of 9 and get 1000000000.

$$6.67+\frac{19890000000000000000}{\left(148.54\times 1000000000\right)^{2}}$$

Multiply 148.54 and 1000000000 to get 148540000000.

$$6.67+\frac{19890000000000000000}{148540000000^{2}}$$

Calculate 148540000000 to the power of 2 and get 22064131600000000000000.

$$6.67+\frac{19890000000000000000}{22064131600000000000000}$$

Reduce the fraction \frac{19890000000000000000}{22064131600000000000000} to lowest terms by extracting and canceling out 400000000000000.

$$6.67+\frac{49725}{55160329}$$

Add 6.67 and \frac{49725}{55160329} to get \frac{36796911943}{5516032900}.

$$\frac{36796911943}{5516032900}$$

Factor

$$\frac{11 \cdot 601 \cdot 5566013}{2 ^ {2} \cdot 5 ^ {2} \cdot 7 ^ {2} \cdot 1061 ^ {2}} = 6\frac{3700714543}{5516032900} = 6.670901463078656$$