Find the numerical equivalent of 7^2 ⋅ 7^3

Answer 1

To find the numerical equivalent of \( 7^2 \cdot 7^3 \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

Applying this property:

\[ 7^2 \cdot 7^3 = 7^{2+3} = 7^5 \]

Now, calculate \( 7^5 \):

\[ 7^5 = 7 \cdot 7 \cdot 7 \cdot 7 \cdot 7 \]

Calculating step-by-step:

1. \( 7^2 = 49 \)
2. \( 7^3 = 7 \cdot 49 = 343 \)
3. Then, \( 7^4 = 7 \cdot 343 = 2401 \)
4. Finally, \( 7^5 = 7 \cdot 2401 = 16807 \)

Thus, the numerical equivalent of \( 7^2 \cdot 7^3 \) is

\[ \boxed{16807} \]