1. I didn't do exercise. Since I had a lot of homework, I didn't have time to do exercise.
2. I didn't exercise. Since I had a lot of homework, I didn't have time to exercise.
3. I didn't take exercise. Since I had a lot of homework, I didn't have time to take exercise.
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Which expressions are grammatical? Are all grammatical? Then, which ones are commonly used?
All are grammatical, but 2 is the very best phrasing.
All three expressions are grammatical and can be used interchangeably. However, the most commonly used expression is "I didn't exercise."
In English, the verb "exercise" can be used both transitively and intransitively. When used intransitively, it means to engage in physical activity to improve health and fitness. In this case, the verb "exercise" does not require an object.
So, the sentence "I didn't exercise" is the most natural and common way to express that you did not engage in physical activity. The phrases "do exercise" and "take exercise" are also grammatically correct, but they are less frequently used in everyday speech.