  For the superelliptic curves of the form $$ (x+1) \cdots(x+i-1)(x+i+1)\cdots
(x+k)=y^\ell$$ with $x,y \in \mathbb{Q}$, $y\neq 0$, $k \geq 3$, $1\leq i\leq
k$, $\ell \geq 2,$ a prime, Das, Laishram, Saradha, and Edis showed that the
superelliptic curve has no rational points for $\ell\geq e^{3^k}$. In fact, the
double exponential bound, obtained in these papers is far from reality. In this
paper, we study the superelliptic curves for small values of $k$. In
particular, we explicitly solve the above equation for $4 \leq k \leq 8.$
