Solve frac{2*79^{2}*(1.6*10^{-19})^{2}cot75^circ}{9*10^9*2*7.6*10^6*1.6*10^-19}

$$\frac { 2 \times 79 ^ { 2 } \times ( 1.6 \times 10 ^ { - 19 } ) ^ { 2 } \cot 75 ^ { \circ } } { 9 \times 10 ^ { 9 } \times 2 \times 7.6 \times 10 ^ { 6 } \times 1.6 \times 10 ^ { - 19 } }$$

Evaluate

$$\frac{5574236366542122569}{1425000000000000000000000000000000000000000000000000}\approx 3.911744819 \cdot 10^{-33}$$

Solution Steps

Evaluate trigonometric functions in the problem

$$\frac{2 \cdot 79 ^ {2} \cdot {(1.6 \cdot 10 ^ {-19})} ^ {2} 0.2679491924311227}{9 \cdot 10 ^ {9} \cdot 2 \cdot 7.6 \cdot 10 ^ {6} \cdot 1.6 \cdot 10 ^ {-19}}$$

To multiply powers of the same base, add their exponents. Add 9 and 6 to get 15.

$$\frac{2\times 79^{2}\times \left(1.6\times 10^{-19}\right)^{2}\times 0.2679491924311227}{9\times 10^{15}\times 2\times 7.6\times 1.6\times 10^{-19}}$$

To multiply powers of the same base, add their exponents. Add 15 and -19 to get -4.

$$\frac{2\times 79^{2}\times \left(1.6\times 10^{-19}\right)^{2}\times 0.2679491924311227}{9\times 10^{-4}\times 2\times 7.6\times 1.6}$$

Cancel out 2 in both numerator and denominator.

$$\frac{0.2679491924311227\times 79^{2}\times \left(1.6\times 10^{-19}\right)^{2}}{1.6\times 7.6\times 9\times 10^{-4}}$$

Calculate 79 to the power of 2 and get 6241.

$$\frac{0.2679491924311227\times 6241\times \left(1.6\times 10^{-19}\right)^{2}}{1.6\times 7.6\times 9\times 10^{-4}}$$

Multiply 0.2679491924311227 and 6241 to get 1672.2709099626367707.

$$\frac{1672.2709099626367707\times \left(1.6\times 10^{-19}\right)^{2}}{1.6\times 7.6\times 9\times 10^{-4}}$$

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

$$\frac{1672.2709099626367707\times \left(1.6\times \frac{1}{10000000000000000000}\right)^{2}}{1.6\times 7.6\times 9\times 10^{-4}}$$

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

$$\frac{1672.2709099626367707\times \left(\frac{1}{6250000000000000000}\right)^{2}}{1.6\times 7.6\times 9\times 10^{-4}}$$

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

$$\frac{1672.2709099626367707\times \frac{1}{39062500000000000000000000000000000000}}{1.6\times 7.6\times 9\times 10^{-4}}$$

Multiply 1672.2709099626367707 and \frac{1}{39062500000000000000000000000000000000} to get \frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000}.

$$\frac{\frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000}}{1.6\times 7.6\times 9\times 10^{-4}}$$

Multiply 1.6 and 7.6 to get 12.16.

$$\frac{\frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000}}{12.16\times 9\times 10^{-4}}$$

Multiply 12.16 and 9 to get 109.44.

$$\frac{\frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000}}{109.44\times 10^{-4}}$$

Calculate 10 to the power of -4 and get \frac{1}{10000}.

$$\frac{\frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000}}{109.44\times \frac{1}{10000}}$$

Multiply 109.44 and \frac{1}{10000} to get \frac{171}{15625}.

$$\frac{\frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000}}{\frac{171}{15625}}$$

Divide \frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000} by \frac{171}{15625} by multiplying \frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000} by the reciprocal of \frac{171}{15625}.

$$\frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000}\times \frac{15625}{171}$$

Multiply \frac{16722709099626367707}{390625000000000000000000000000000000000000000000000000} and \frac{15625}{171} to get \frac{5574236366542122569}{1425000000000000000000000000000000000000000000000000}.

$$\frac{5574236366542122569}{1425000000000000000000000000000000000000000000000000}$$

Factor

$$\frac{20887 \cdot 42761716607 \cdot 79 ^ {2}}{3 \cdot 19 \cdot 2 ^ {48} \cdot 5 ^ {50}} = 3.911744818626051 \times 10^{-33}$$