Solve for: 2^{(n+3)}-:2^{(6n+1)}

Expression: 2^(n+3)-:2^(6n+1)

Write the problem as a mathematical expression

$2^{n + 3} \div 2^{6n + 1}$

Rewrite the division as a fraction

$\frac{2^{n + 3}}{2^{6n + 1}}$

Factor $2^{6n + 1}$

$\frac{2^{6n + 1} \cdot 2^{n + 3 - \left(6n + 1\right)}}{2^{6n + 1}}$

Multiply by $1$

$\frac{2^{6n + 1} \cdot 2^{n + 3 - \left(6n + 1\right)}}{2^{6n + 1} \cdot 1}$

Cancel the common factor

$\frac{2^{6n + 1} \cdot 2^{n + 3 - \left(6n + 1\right)}}{2^{6n + 1} \cdot 1}$

Rewrite the expression

$\frac{2^{n + 3 - \left(6n + 1\right)}}{1}$

Divide $2^{n + 3 - \left(6n + 1\right)}$

$2^{n + 3 - \left(6n + 1\right)}$

Apply the distributive property

$2^{n + 3 - \left(6n\right) - 1 \cdot 1}$

Multiply $6$

$2^{n + 3 - 6n - 1 \cdot 1}$

Multiply $ - 1$

$2^{n + 3 - 6n - 1}$

Subtract $6n$

$2^{ - 5n + 3 - 1}$

Subtract $1$

$2^{ - 5n + 2}$