Solve 6.67*10^-14*7.4*10^12/(1740*10^11)^2

$$\frac { 6.67 \times 10 ^ { - 14 } \times 7.4 \times 10 ^ { 12 } } { ( 1740 \times 10 ^ { 11 } ) ^ { 2 } }$$

Evaluate

$$\frac{851}{52200000000000000000000000000000}\approx 1.630268199 \cdot 10^{-29}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -14 and 12 to get -2.

$$\frac{6.67\times 10^{-2}\times 7.4}{\left(1740\times 10^{11}\right)^{2}}$$

Calculate 10 to the power of -2 and get \frac{1}{100}.

$$\frac{6.67\times \frac{1}{100}\times 7.4}{\left(1740\times 10^{11}\right)^{2}}$$

Multiply 6.67 and \frac{1}{100} to get \frac{667}{10000}.

$$\frac{\frac{667}{10000}\times 7.4}{\left(1740\times 10^{11}\right)^{2}}$$

Multiply \frac{667}{10000} and 7.4 to get \frac{24679}{50000}.

$$\frac{\frac{24679}{50000}}{\left(1740\times 10^{11}\right)^{2}}$$

Calculate 10 to the power of 11 and get 100000000000.

$$\frac{\frac{24679}{50000}}{\left(1740\times 100000000000\right)^{2}}$$

Multiply 1740 and 100000000000 to get 174000000000000.

$$\frac{\frac{24679}{50000}}{174000000000000^{2}}$$

Calculate 174000000000000 to the power of 2 and get 30276000000000000000000000000.

$$\frac{\frac{24679}{50000}}{30276000000000000000000000000}$$

Express \frac{\frac{24679}{50000}}{30276000000000000000000000000} as a single fraction.

$$\frac{24679}{50000\times 30276000000000000000000000000}$$

Multiply 50000 and 30276000000000000000000000000 to get 1513800000000000000000000000000000.

$$\frac{24679}{1513800000000000000000000000000000}$$

Reduce the fraction \frac{24679}{1513800000000000000000000000000000} to lowest terms by extracting and canceling out 29.

$$\frac{851}{52200000000000000000000000000000}$$

Factor

$$\frac{23 \cdot 37}{29 \cdot 2 ^ {30} \cdot 3 ^ {2} \cdot 5 ^ {29}} = 1.6302681992337167 \times 10^{-29}$$