When justice lewis powell stated that racial and ethnic distinctions require the most exacting judicial examination he meant these qualities required

When Justice Lewis Powell stated that racial and ethnic distinctions require the most exacting judicial examination, he meant these qualities required extremely precise consideration.

Explanation:

In the case of Allan Bakke being rejected admission in the University of California, Davis, in 1973 and 1974, he filed a case against the university citing that they had no right to deny admission to any student with regards to age when there are less qualified students from the minority section who are admitted. This became into what is now famously known as the case of the Regeants of the University of California v. Bakke. The case was transferred to the state supreme court due to it's involvement with the racial issue which was of prominence during that time. Justice Powell was part of the team working on the case.  The verdict of the court was that Bakke be granted admission and that universities/ educational institutions remove the special reservations policy and instead allow admission to students based on their merit and not based on race or minority status. And if any issue of racial and ethnic distinctions arise, they should be dealt with in the most exacting judicial examination required so that there is no discrimination involved. It doesn't mean that the issue of race or ethnicity be completely scraped but it should be dealt with extremely precise consideration.

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it is an infinitive phrase with a subject.