To simplify the expression \( \frac{t^{400}}{t^{100}} \) using the quotient rule of integer exponents, we can apply the rule:
\[ \frac{a^m}{a^n} = a^{m-n} \]
In this case:
- \( a = t \)
- \( m = 400 \)
- \( n = 100 \)
Now, applying the rule:
\[ \frac{t^{400}}{t^{100}} = t^{400 - 100} = t^{300} \]
So, the simplification of the expression \( \frac{t^{400}}{t^{100}} \) is \( t^{300} \).
Therefore, the answer is \( t^{300} \).