Solve 9*10^9left(1.610^-19right)^2/6.6710^-119.1{10^-311.66{10}^-27}

$$\frac{ 9 \times { 10 }^{ 9 } { \left(1.6 { 10 }^{ -19 } \right) }^{ 2 } }{ 6.67 { 10 }^{ -11 } 9.1 { 10 }^{ -31 } 1.66 { 10 }^{ -27 } }$$

Evaluate

$$\frac{11520000000000000000000000000000000000000000000}{5037851}\approx 2.286689305 \cdot 10^{39}$$

Solution Steps

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

$$\frac{9\times 10^{9}\times \left(1.6\times 10^{-19}\right)^{2}}{6.67\times 10^{-42}\times 9.1\times 1.66\times 10^{-27}}$$

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

$$\frac{9\times 10^{9}\times \left(1.6\times 10^{-19}\right)^{2}}{6.67\times 10^{-69}\times 9.1\times 1.66}$$

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

$$\frac{9\times 10^{78}\times \left(1.6\times 10^{-19}\right)^{2}}{1.66\times 6.67\times 9.1}$$

Calculate 10 to the power of 78 and get 1000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{9\times 1000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{1.66\times 6.67\times 9.1}$$

Multiply 9 and 1000000000000000000000000000000000000000000000000000000000000000000000000000000 to get 9000000000000000000000000000000000000000000000000000000000000000000000000000000.

$$\frac{9000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times 10^{-19}\right)^{2}}{1.66\times 6.67\times 9.1}$$

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

$$\frac{9000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(1.6\times \frac{1}{10000000000000000000}\right)^{2}}{1.66\times 6.67\times 9.1}$$

Multiply 1.6 and \frac{1}{10000000000000000000} to get \frac{1}{6250000000000000000}.

$$\frac{9000000000000000000000000000000000000000000000000000000000000000000000000000000\times \left(\frac{1}{6250000000000000000}\right)^{2}}{1.66\times 6.67\times 9.1}$$

Calculate \frac{1}{6250000000000000000} to the power of 2 and get \frac{1}{39062500000000000000000000000000000000}.

$$\frac{9000000000000000000000000000000000000000000000000000000000000000000000000000000\times \frac{1}{39062500000000000000000000000000000000}}{1.66\times 6.67\times 9.1}$$

Multiply 9000000000000000000000000000000000000000000000000000000000000000000000000000000 and \frac{1}{39062500000000000000000000000000000000} to get 230400000000000000000000000000000000000000.

$$\frac{230400000000000000000000000000000000000000}{1.66\times 6.67\times 9.1}$$

Multiply 1.66 and 6.67 to get 11.0722.

$$\frac{230400000000000000000000000000000000000000}{11.0722\times 9.1}$$

Multiply 11.0722 and 9.1 to get 100.75702.

$$\frac{230400000000000000000000000000000000000000}{100.75702}$$

Expand \frac{230400000000000000000000000000000000000000}{100.75702} by multiplying both numerator and the denominator by 100000.

$$\frac{23040000000000000000000000000000000000000000000}{10075702}$$

Reduce the fraction \frac{23040000000000000000000000000000000000000000000}{10075702} to lowest terms by extracting and canceling out 2.

$$\frac{11520000000000000000000000000000000000000000000}{5037851}$$

Factor

$$\frac{2 ^ {50} \cdot 3 ^ {2} \cdot 5 ^ {43}}{7 \cdot 13 \cdot 23 \cdot 29 \cdot 83} = 2.2866893046261194 \times 10^{39}\frac{3795180}{5037851} = 2.2866893046261194 \times 10^{39}$$