She is a very capable black woman.
If that is an effort to write a politically correct non-racist sentence, you have nearly succeeded. It would be better without the word "black". Otherwise, it might be thought of as having a condescending "attitude", as if it were unusual for most black women to be capable.
I do not see any prejudice related to age in your sentence.
It's important to be mindful of the language we use to ensure that we promote equality and avoid perpetuating stereotypes. When describing someone's capabilities, it is generally best to focus on their individual achievements and skills rather than emphasizing their race or gender.
To rephrase the sentence in a more politically correct and non-racist way while avoiding potential condescension, you can simply say, "She is a very capable woman." By omitting the reference to race, it removes any implication that her capabilities are exceptional based on her race. It is important to remember that individuals should be judged on their individual merits rather than generalizations based on their race, gender, or other defining characteristics.
Regarding age prejudice, the original sentence does not mention age, so it is not a factor in this specific context. However, age prejudice can also be an issue that should be avoided when discussing someone's capabilities or achievements. It is essential to focus on a person's abilities rather than making assumptions based on age or any other characteristic.