We develop a scale transformed version of the power prior to accommodate settings in which the historical data and the current data involve different data types, such as binary and continuous data. This situation arises often in clinical trials, for example, when the historical data involves binary response data and the current data may be time-to-event or some other continuous outcome. The traditional Power Prior proposed by Ibrahim and Chen (2000) does not account for different data types in the context discussed here. Thus, a new type of power prior needs to be formulated in these settings, which we call the scale transformed power prior. The scale transformed power prior is constructed so that the information matrix based the current data likelihood is appropriately scaled by the information matrix from the power prior, thereby shifting the scale of the parameter vector from the historical data to the new data. Several examples are presented to motivate the scale transformation and several simulation studies are presented to show the advantages in performance of the scale transformed power prior over the power prior and other priors.