Expressing a fraction in the simplest form means to simplify common factor in the numerator and the denominator.
To do so, let's find the prime factorization of both:
[tex]8=2^3=2\cdot 2\cdot 2,\quad 14=2\cdot 7[/tex]
So, we can write the fraction as
[tex]\dfrac{8}{14}=\dfrac{2\cdot 2\cdot 2}{2\cdot 7}[/tex]
We can simplify (i.e. cancel) a factor 2 appearing both in the numerator and denominator. We're left with
[tex]\dfrac{8}{14}=\dfrac{2\cdot 2}{7}=\dfrac{4}{7}[/tex]