To change the color of a shape in PowerPoint using the Eyedropper tool, follow these steps:

1. Select the shape you want to change the color of.
2. Click the 'Shape Fill' or 'Shape Outline' option located on the Drawing Tools contextual tab.
3. Click the 'Eyedropper Tool' located in the same panel.
4. Once the Eyedropper Tool is selected, click on a new color you desire for the shape.
5. Your shape will automatically have its color changed to the new color you have selected.