To find the numerical equivalent of \( 7^2 \cdot 7^3 \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).
So,
\[ 7^2 \cdot 7^3 = 7^{2+3} = 7^5 \]
Now, you can calculate \( 7^5 \):
\[ 7^5 = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \] Calculating it step by step:
\[ 7^2 = 49 \] \[ 7^3 = 7 \cdot 49 = 343 \] \[ 7^4 = 7 \cdot 343 = 2401 \] \[ 7^5 = 7 \cdot 2401 = 16807 \]
Thus, the numerical equivalent of \( 7^2 \cdot 7^3 \) is \( 16807 \).