Exponent System Value
Number Theory
If $2^x \times 3^y = 108$, and $x + y = 7$, find the exact value of $\left(\frac{3}{2}\right)^x$.
The answer is in the form $\frac{\alpha}{\beta}$ for coprime integers $\alpha$ and $\beta$. Input the answer as the sum $\alpha +\beta$.