Solve frac{9*10^{8}*(16*10^{-19})^2}{667*10^-11*91*10^-31*166*10^-27}

$$\frac { 9 \times 10 ^ { 8 } \times ( 16 \times 10 ^ { - 19 } ) ^ { 2 } } { 667 \times 10 ^ { - 11 } \times 91 \times 10 ^ { - 31 } \times 166 \times 10 ^ { - 27 } }$$

Evaluate

$$\frac{1152000000000000000000000000000000000000000}{5037851}\approx 2.286689305 \cdot 10^{35}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -11 and -31 to get -42.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-42}\times 91\times 166\times 10^{-27}}$$

To multiply powers of the same base, add their exponents. Add -42 and -27 to get -69.

$$\frac{9\times 10^{8}\times \left(16\times 10^{-19}\right)^{2}}{667\times 10^{-69}\times 91\times 166}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{9\times 10^{77}\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Calculate 10 to the power of 77 and get 100000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{9\times 100000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Multiply 9 and 100000000000000000000000000000000000000000000000000000000000000000000000000000 to get 900000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times 10^{-19}\right)^{2}}{91\times 166\times 667}$$

Calculate 10 to the power of -19 and get \frac{1}{10000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(16\times \frac{1}{10000000000000000000}\right)^{2}}{91\times 166\times 667}$$

Multiply 16 and \frac{1}{10000000000000000000} to get \frac{1}{625000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{625000000000000000}\right)^{2}}{91\times 166\times 667}$$

Calculate \frac{1}{625000000000000000} to the power of 2 and get \frac{1}{390625000000000000000000000000000000}.

$$\frac{900000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{390625000000000000000000000000000000}}{91\times 166\times 667}$$

Multiply 900000000000000000000000000000000000000000000000000000000000000000000000000000 and \frac{1}{390625000000000000000000000000000000} to get 2304000000000000000000000000000000000000000.

$$\frac{2304000000000000000000000000000000000000000}{91\times 166\times 667}$$

Multiply 91 and 166 to get 15106.

$$\frac{2304000000000000000000000000000000000000000}{15106\times 667}$$

Multiply 15106 and 667 to get 10075702.

$$\frac{2304000000000000000000000000000000000000000}{10075702}$$

Reduce the fraction \frac{2304000000000000000000000000000000000000000}{10075702} to lowest terms by extracting and canceling out 2.

$$\frac{1152000000000000000000000000000000000000000}{5037851}$$

Factor

$$\frac{2 ^ {46} \cdot 3 ^ {2} \cdot 5 ^ {39}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 2.2866893046261194 \times 10^{35}\frac{336198}{5037851} = 2.2866893046261194 \times 10^{35}$$