Solve N_{r}=6.022*10^-23*18.63/196.9exp[0.98/(8.62*10^-5)(1023)]

$$N _ { r } = \frac { 6.022 \times 10 ^ { - 23 } \cdot 18.63 } { 196.9 } \exp [ \frac { 0.98 } { ( 8.62 \times 10 ^ { - 5 } ) ( 1023 ) } ]$$

Solve for p (complex solution)

$$\left\{\begin{matrix}p=\frac{1446929495000000000000000000000N_{r}}{91621719ex}\text{, }&x\neq 0\\p\in \mathrm{C}\text{, }&N_{r}=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 10 to the power of -23 and get \frac{1}{100000000000000000000000}.

$$N_{r}=\frac{6.022\times \frac{1}{100000000000000000000000}\times 18.63}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply 6.022 and \frac{1}{100000000000000000000000} to get \frac{3011}{50000000000000000000000000}.

$$N_{r}=\frac{\frac{3011}{50000000000000000000000000}\times 18.63}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply \frac{3011}{50000000000000000000000000} and 18.63 to get \frac{5609493}{5000000000000000000000000000}.

$$N_{r}=\frac{\frac{5609493}{5000000000000000000000000000}}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Express \frac{\frac{5609493}{5000000000000000000000000000}}{196.9} as a single fraction.

$$N_{r}=\frac{5609493}{5000000000000000000000000000\times 196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply 5000000000000000000000000000 and 196.9 to get 984500000000000000000000000000.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{8.62\times \frac{1}{100000}\times 1023}$$

Multiply 8.62 and \frac{1}{100000} to get \frac{431}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{\frac{431}{5000000}\times 1023}$$

Multiply \frac{431}{5000000} and 1023 to get \frac{440913}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{\frac{440913}{5000000}}$$

Divide 0.98 by \frac{440913}{5000000} by multiplying 0.98 by the reciprocal of \frac{440913}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times 0.98\times \frac{5000000}{440913}$$

Multiply 0.98 and \frac{5000000}{440913} to get \frac{4900000}{440913}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{4900000}{440913}$$

Multiply \frac{5609493}{984500000000000000000000000000} and \frac{4900000}{440913} to get \frac{91621719}{1446929495000000000000000000000}.

$$N_{r}=\frac{91621719}{1446929495000000000000000000000}exp$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{91621719}{1446929495000000000000000000000}exp=N_{r}$$

The equation is in standard form.

$$\frac{91621719ex}{1446929495000000000000000000000}p=N_{r}$$

Divide both sides by \frac{91621719}{1446929495000000000000000000000}ex.

$$\frac{1446929495000000000000000000000\times \frac{91621719ex}{1446929495000000000000000000000}p}{91621719ex}=\frac{1446929495000000000000000000000N_{r}}{91621719ex}$$

Dividing by \frac{91621719}{1446929495000000000000000000000}ex undoes the multiplication by \frac{91621719}{1446929495000000000000000000000}ex.

$$p=\frac{1446929495000000000000000000000N_{r}}{91621719ex}$$

Solve for N_r

$$N_{r}=\frac{91621719epx}{1446929495000000000000000000000}$$

Solution Steps

Calculate 10 to the power of -23 and get \frac{1}{100000000000000000000000}.

$$N_{r}=\frac{6.022\times \frac{1}{100000000000000000000000}\times 18.63}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply 6.022 and \frac{1}{100000000000000000000000} to get \frac{3011}{50000000000000000000000000}.

$$N_{r}=\frac{\frac{3011}{50000000000000000000000000}\times 18.63}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply \frac{3011}{50000000000000000000000000} and 18.63 to get \frac{5609493}{5000000000000000000000000000}.

$$N_{r}=\frac{\frac{5609493}{5000000000000000000000000000}}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Express \frac{\frac{5609493}{5000000000000000000000000000}}{196.9} as a single fraction.

$$N_{r}=\frac{5609493}{5000000000000000000000000000\times 196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply 5000000000000000000000000000 and 196.9 to get 984500000000000000000000000000.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{8.62\times \frac{1}{100000}\times 1023}$$

Multiply 8.62 and \frac{1}{100000} to get \frac{431}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{\frac{431}{5000000}\times 1023}$$

Multiply \frac{431}{5000000} and 1023 to get \frac{440913}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{\frac{440913}{5000000}}$$

Divide 0.98 by \frac{440913}{5000000} by multiplying 0.98 by the reciprocal of \frac{440913}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times 0.98\times \frac{5000000}{440913}$$

Multiply 0.98 and \frac{5000000}{440913} to get \frac{4900000}{440913}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{4900000}{440913}$$

Multiply \frac{5609493}{984500000000000000000000000000} and \frac{4900000}{440913} to get \frac{91621719}{1446929495000000000000000000000}.

$$N_{r}=\frac{91621719}{1446929495000000000000000000000}exp$$

Solve for p

$$\left\{\begin{matrix}p=\frac{1446929495000000000000000000000N_{r}}{91621719ex}\text{, }&x\neq 0\\p\in \mathrm{R}\text{, }&N_{r}=0\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Calculate 10 to the power of -23 and get \frac{1}{100000000000000000000000}.

$$N_{r}=\frac{6.022\times \frac{1}{100000000000000000000000}\times 18.63}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply 6.022 and \frac{1}{100000000000000000000000} to get \frac{3011}{50000000000000000000000000}.

$$N_{r}=\frac{\frac{3011}{50000000000000000000000000}\times 18.63}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply \frac{3011}{50000000000000000000000000} and 18.63 to get \frac{5609493}{5000000000000000000000000000}.

$$N_{r}=\frac{\frac{5609493}{5000000000000000000000000000}}{196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Express \frac{\frac{5609493}{5000000000000000000000000000}}{196.9} as a single fraction.

$$N_{r}=\frac{5609493}{5000000000000000000000000000\times 196.9}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Multiply 5000000000000000000000000000 and 196.9 to get 984500000000000000000000000000.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{8.62\times 10^{-5}\times 1023}$$

Calculate 10 to the power of -5 and get \frac{1}{100000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{8.62\times \frac{1}{100000}\times 1023}$$

Multiply 8.62 and \frac{1}{100000} to get \frac{431}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{\frac{431}{5000000}\times 1023}$$

Multiply \frac{431}{5000000} and 1023 to get \frac{440913}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{0.98}{\frac{440913}{5000000}}$$

Divide 0.98 by \frac{440913}{5000000} by multiplying 0.98 by the reciprocal of \frac{440913}{5000000}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times 0.98\times \frac{5000000}{440913}$$

Multiply 0.98 and \frac{5000000}{440913} to get \frac{4900000}{440913}.

$$N_{r}=\frac{5609493}{984500000000000000000000000000}exp\times \frac{4900000}{440913}$$

Multiply \frac{5609493}{984500000000000000000000000000} and \frac{4900000}{440913} to get \frac{91621719}{1446929495000000000000000000000}.

$$N_{r}=\frac{91621719}{1446929495000000000000000000000}exp$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{91621719}{1446929495000000000000000000000}exp=N_{r}$$

The equation is in standard form.

$$\frac{91621719ex}{1446929495000000000000000000000}p=N_{r}$$

Divide both sides by \frac{91621719}{1446929495000000000000000000000}ex.

$$\frac{1446929495000000000000000000000\times \frac{91621719ex}{1446929495000000000000000000000}p}{91621719ex}=\frac{1446929495000000000000000000000N_{r}}{91621719ex}$$

Dividing by \frac{91621719}{1446929495000000000000000000000}ex undoes the multiplication by \frac{91621719}{1446929495000000000000000000000}ex.

$$p=\frac{1446929495000000000000000000000N_{r}}{91621719ex}$$