Is the fraction 38 in lowest terms?

Yes, the fraction $\frac{3}{8}$ is in lowest form as there is no whole number by which we can divide the numerator and denominator.

3 is a prime number so the fraction is in what people call its simplest form.

Yes the fraction $\frac{3}{8}$ is in lowest terms because the numerator is 3, a prime number, and whenever there is a prime number in a fraction in either numerator or denominator, it cannot be cut in lower except when the prime number is a factor of the other.
Hope you understood.