Summary: A pebbling move on a connected graph \(G\) is taking two pebbles off of one vertex and placing one of them on an adjacent vertex. For a connected graph \(G\), \(G^p\) \((p>1)\) is the graph obtained from \(G\) by adding the edges \((u, v)\) to \(G\) whenever \(2\leq\text{dist}(u, v)\leq p\) in \(G\). And the pebbling exponent of a graph \(G\) to be the least power of \(p\) such that the pebbling number of \(G^p\) is equal to the number of vertices of \(G\). We compute the pebbling number of fourth power of paths so that the pebbling exponents of some paths are calculated.