Solve 667*10^-14*74*10^12/(1740*10^11)^2

$$\frac { 667 \times 10 ^ { - 14 } \times 74 \times 10 ^ { 12 } } { ( 1740 \times 10 ^ { 11 } ) ^ { 2 } }$$

Evaluate

$$\frac{851}{52200000000000000000000000000}\approx 1.630268199 \cdot 10^{-26}$$

Solution Steps

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

$$\frac{667\times 10^{-2}\times 74}{\left(1740\times 10^{11}\right)^{2}}$$

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

$$\frac{667\times \frac{1}{100}\times 74}{\left(1740\times 10^{11}\right)^{2}}$$

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

$$\frac{\frac{667}{100}\times 74}{\left(1740\times 10^{11}\right)^{2}}$$

Multiply \frac{667}{100} and 74 to get \frac{24679}{50}.

$$\frac{\frac{24679}{50}}{\left(1740\times 10^{11}\right)^{2}}$$

Calculate 10 to the power of 11 and get 100000000000.

$$\frac{\frac{24679}{50}}{\left(1740\times 100000000000\right)^{2}}$$

Multiply 1740 and 100000000000 to get 174000000000000.

$$\frac{\frac{24679}{50}}{174000000000000^{2}}$$

Calculate 174000000000000 to the power of 2 and get 30276000000000000000000000000.

$$\frac{\frac{24679}{50}}{30276000000000000000000000000}$$

Express \frac{\frac{24679}{50}}{30276000000000000000000000000} as a single fraction.

$$\frac{24679}{50\times 30276000000000000000000000000}$$

Multiply 50 and 30276000000000000000000000000 to get 1513800000000000000000000000000.

$$\frac{24679}{1513800000000000000000000000000}$$

Reduce the fraction \frac{24679}{1513800000000000000000000000000} to lowest terms by extracting and canceling out 29.

$$\frac{851}{52200000000000000000000000000}$$

Factor

$$\frac{23 \cdot 37}{2 ^ {27} \cdot 3 ^ {2} \cdot 5 ^ {26} \cdot 29} = 1.6302681992337162 \times 10^{-26}$$