To simplify the expression \( t^{400} \cdot t^{100} \) using the properties of exponents, you can apply the Product Rule of exponents, which states that when multiplying like bases, you add the exponents:
\[ t^{a} \cdot t^{b} = t^{a + b} \]
In this case, \( a = 400 \) and \( b = 100 \):
\[ t^{400} \cdot t^{100} = t^{400 + 100} = t^{500} \]
Thus, the simplified expression is:
\[ t^{500} \]
So the correct response is:
t superscript 500 baseline.