In this paper, we consider a generalization of the modified slash distribution. We define the new family through the quotient between an elliptically distributed random variable and the power of an exponential random variable with parameter equals to 2, both independent. We use the same idea to extend the model for the multivariate case and study general important properties from the resultant family. We perform inference by the method of moments and maximum likelihood. We present a simulation study which indicates satisfactory parameter recovery by using the estimation approaches. Illustrations reveals that it has potential for doing well in real problems.