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The process to establish a maximum default value for a slicer in Power BI is as follows:

1. Open Power BI Desktop and select the report page that contains the slicer.

2. Click on the slicer to select it.

3. In the Visualizations pane, click on the Format button (paint roller icon) to open the Format pane.

4. In the Format pane, expand the Data options section.

5. Scroll down to the Min and Max options and enter the maximum value that you want to set as the default for the slicer.

6. Click on the Apply button to apply the changes.

7. Save and publish the report to make the changes visible to the report consumers.

After the above steps, the slicer will have the maximum default value set, and it will not allow any value greater than the maximum value selected.