Solve frac{(e*6*10^{-19})^2*(0.15)^2*(1.5)^2}{2*1.6*10^-27}

$$\frac { ( e \cdot 6 \times 10 ^ { - 19 } ) ^ { 2 } \times ( 0.15 ) ^ { 2 } \times ( 1.5 ) ^ { 2 } } { 2 \times 1.6 \times 10 ^ { - 27 } }$$

Evaluate

$$\frac{729e^{2}}{128000000000000}\approx 4.208298356 \cdot 10^{-11}$$

Solution Steps

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

$$\frac{\left(e\times 6\times \frac{1}{10000000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Multiply 6 and \frac{1}{10000000000000000000} to get \frac{3}{5000000000000000000}.

$$\frac{\left(e\times \frac{3}{5000000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Expand \left(e\times \frac{3}{5000000000000000000}\right)^{2}.

$$\frac{e^{2}\times \left(\frac{3}{5000000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Calculate \frac{3}{5000000000000000000} to the power of 2 and get \frac{9}{25000000000000000000000000000000000000}.

$$\frac{e^{2}\times \frac{9}{25000000000000000000000000000000000000}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Calculate 0.15 to the power of 2 and get 0.0225.

$$\frac{e^{2}\times \frac{9}{25000000000000000000000000000000000000}\times 0.0225\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Multiply \frac{9}{25000000000000000000000000000000000000} and 0.0225 to get \frac{81}{10000000000000000000000000000000000000000}.

$$\frac{e^{2}\times \frac{81}{10000000000000000000000000000000000000000}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$\frac{e^{2}\times \frac{81}{10000000000000000000000000000000000000000}\times 2.25}{2\times 1.6\times 10^{-27}}$$

Multiply \frac{81}{10000000000000000000000000000000000000000} and 2.25 to get \frac{729}{40000000000000000000000000000000000000000}.

$$\frac{e^{2}\times \frac{729}{40000000000000000000000000000000000000000}}{2\times 1.6\times 10^{-27}}$$

Multiply 2 and 1.6 to get 3.2.

$$\frac{e^{2}\times \frac{729}{40000000000000000000000000000000000000000}}{3.2\times 10^{-27}}$$

Calculate 10 to the power of -27 and get \frac{1}{1000000000000000000000000000}.

$$\frac{e^{2}\times \frac{729}{40000000000000000000000000000000000000000}}{3.2\times \frac{1}{1000000000000000000000000000}}$$

Multiply 3.2 and \frac{1}{1000000000000000000000000000} to get \frac{1}{312500000000000000000000000}.

$$\frac{e^{2}\times \frac{729}{40000000000000000000000000000000000000000}}{\frac{1}{312500000000000000000000000}}$$

Divide e^{2}\times \frac{729}{40000000000000000000000000000000000000000} by \frac{1}{312500000000000000000000000} by multiplying e^{2}\times \frac{729}{40000000000000000000000000000000000000000} by the reciprocal of \frac{1}{312500000000000000000000000}.

$$e^{2}\times \frac{729}{40000000000000000000000000000000000000000}\times 312500000000000000000000000$$

Multiply \frac{729}{40000000000000000000000000000000000000000} and 312500000000000000000000000 to get \frac{729}{128000000000000}.

$$e^{2}\times \frac{729}{128000000000000}$$

Expand

$$\frac{729e^{2}}{128000000000000}$$

Solution Steps

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

$$\frac{\left(e\times 6\times \frac{1}{10000000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Multiply 6 and \frac{1}{10000000000000000000} to get \frac{3}{5000000000000000000}.

$$\frac{\left(e\times \frac{3}{5000000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Expand \left(e\times \frac{3}{5000000000000000000}\right)^{2}.

$$\frac{e^{2}\times \left(\frac{3}{5000000000000000000}\right)^{2}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Calculate \frac{3}{5000000000000000000} to the power of 2 and get \frac{9}{25000000000000000000000000000000000000}.

$$\frac{e^{2}\times \frac{9}{25000000000000000000000000000000000000}\times 0.15^{2}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Calculate 0.15 to the power of 2 and get 0.0225.

$$\frac{e^{2}\times \frac{9}{25000000000000000000000000000000000000}\times 0.0225\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Multiply \frac{9}{25000000000000000000000000000000000000} and 0.0225 to get \frac{81}{10000000000000000000000000000000000000000}.

$$\frac{e^{2}\times \frac{81}{10000000000000000000000000000000000000000}\times 1.5^{2}}{2\times 1.6\times 10^{-27}}$$

Calculate 1.5 to the power of 2 and get 2.25.

$$\frac{e^{2}\times \frac{81}{10000000000000000000000000000000000000000}\times 2.25}{2\times 1.6\times 10^{-27}}$$

Multiply \frac{81}{10000000000000000000000000000000000000000} and 2.25 to get \frac{729}{40000000000000000000000000000000000000000}.

$$\frac{e^{2}\times \frac{729}{40000000000000000000000000000000000000000}}{2\times 1.6\times 10^{-27}}$$

Multiply 2 and 1.6 to get 3.2.

$$\frac{e^{2}\times \frac{729}{40000000000000000000000000000000000000000}}{3.2\times 10^{-27}}$$

Calculate 10 to the power of -27 and get \frac{1}{1000000000000000000000000000}.

$$\frac{e^{2}\times \frac{729}{40000000000000000000000000000000000000000}}{3.2\times \frac{1}{1000000000000000000000000000}}$$

Multiply 3.2 and \frac{1}{1000000000000000000000000000} to get \frac{1}{312500000000000000000000000}.

$$\frac{e^{2}\times \frac{729}{40000000000000000000000000000000000000000}}{\frac{1}{312500000000000000000000000}}$$

Divide e^{2}\times \frac{729}{40000000000000000000000000000000000000000} by \frac{1}{312500000000000000000000000} by multiplying e^{2}\times \frac{729}{40000000000000000000000000000000000000000} by the reciprocal of \frac{1}{312500000000000000000000000}.

$$e^{2}\times \frac{729}{40000000000000000000000000000000000000000}\times 312500000000000000000000000$$

Multiply \frac{729}{40000000000000000000000000000000000000000} and 312500000000000000000000000 to get \frac{729}{128000000000000}.

$$e^{2}\times \frac{729}{128000000000000}$$