Question

hen multiplying powers with the same base, add the exponents:
7
2
⋅
7
3
=
7
2
+
3
=
7
5

Answer 1

Correct. In general, for a nonzero base a and integers m,n:
a^m · a^n = a^{m+n}.

Reason: a^m means a multiplied by itself m times and a^n is a multiplied n times, so together that's a multiplied m+n times.

Example: 7^2 · 7^3 = 7^{2+3} = 7^5. Numerically, 49 · 343 = 16,807, and 7^5 = 16,807.