Solve 2^m+1*a^m+n=a^8*b

$$2 ^ { m + 1 } \cdot a ^ { m + n } = a ^ { 8 } \cdot b$$

Solve for b (complex solution)

$$\left\{\begin{matrix}b=2^{m+1}a^{m+n-8}\text{, }&a\neq 0\\b\in \mathrm{C}\text{, }&m\neq -n\text{ and }a=0\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a^{8}b=2^{m+1}a^{m+n}$$

Divide both sides by a^{8}.

$$\frac{a^{8}b}{a^{8}}=\frac{2^{m+1}a^{m+n}}{a^{8}}$$

Dividing by a^{8} undoes the multiplication by a^{8}.

$$b=\frac{2^{m+1}a^{m+n}}{a^{8}}$$

Divide a^{m+n}\times 2^{1+m} by a^{8}.

$$b=2^{m+1}a^{m+n-8}$$

Solve for b

$$\left\{\begin{matrix}b=2^{m+1}a^{m+n-8}\text{, }&a>0\text{ or }\left(Denominator(m+n)\text{bmod}2=1\text{ and }a<0\right)\\b\in \mathrm{R}\text{, }&a=0\text{ and }m>-n\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$a^{8}b=2^{m+1}a^{m+n}$$

Divide both sides by a^{8}.

$$\frac{a^{8}b}{a^{8}}=\frac{2^{m+1}a^{m+n}}{a^{8}}$$

Dividing by a^{8} undoes the multiplication by a^{8}.

$$b=\frac{2^{m+1}a^{m+n}}{a^{8}}$$

Divide a^{m+n}\times 2^{1+m} by a^{8}.

$$b=2^{m+1}a^{m+n-8}$$