Question

Find the numerical equivalent of 7 to the second power times 7 to the third power

Answer 1

To find the numerical equivalent of \( 7^2 \times 7^3 \), you can use the property of exponents that states:

\[
a^m \times a^n = a^{m+n}
\]

In this case, \( a = 7 \), \( m = 2 \), and \( n = 3 \). Using the property, we combine the exponents:

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

Now, we need to calculate \( 7^5 \):

\[
7^5 = 7 \times 7 \times 7 \times 7 \times 7
\]

Calculating this step-by-step:

- \( 7 \times 7 = 49 \)
- \( 49 \times 7 = 343 \)
- \( 343 \times 7 = 2401 \)
- \( 2401 \times 7 = 16807 \)

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

\[
\boxed{16807}
\]