To simplify the expression \( h^3 \cdot h^7 \), you can use the laws of exponents. Specifically, when you multiply two expressions with the same base, you add their exponents:
\[ h^a \cdot h^b = h^{a+b} \]
Applying this rule:
\[ h^3 \cdot h^7 = h^{3+7} = h^{10} \]
So, the simplified expression is \( h^{10} \).