To find the numerical equivalent of \( 7 \cdot 7^3 \), we can simplify the expression using the properties of exponents.
Recall that \( a^m \cdot a^n = a^{m+n} \). In this case:
\[ 7 \cdot 7^3 = 7^1 \cdot 7^3 = 7^{1+3} = 7^4 \]
Now we need to calculate \( 7^4 \):
\[ 7^4 = 7 \cdot 7 \cdot 7 \cdot 7 \]
Calculating this step by step:
\[ 7 \cdot 7 = 49 \]
\[ 49 \cdot 7 = 343 \]
\[ 343 \cdot 7 = 2401 \]
Thus, \( 7^4 = 2401 \).
Therefore, the numerical equivalent of \( 7 \cdot 7^3 \) is \( \boxed{2401} \).