Hi, 

This is powdery mildew which is very common on crapemyrtle trees especially in the heat and humidity. 

Disease resistant varieties are best but most crapemyrtles can still get some powdery mildew. It seems like the dark leaved ones are more susceptible but that could be due to the planting location. Pruning to have more air circulation through the plants can be helpful but it shouldn't overall affect the health of the plants if it isn't too severe. Sometimes horticultural oil can help but in high heat it should be avoided, just read the label before applying and follow timing directions. Fungicides aren't necessarily recommended as they can have harmful affects on pollinator insects and would need to be used continuously. Also they are only preventative and not curative so would need to be applied before the infection starts. Long term use of fungicides can also be harmful to the beneficial soil microbes are the base of the plant so they tend to not be a practical management solution. 

Emily