Question

Simplifying a Product of Powers
Which shows the correct simplification of product of powers?

78 · 7-4 = 78· (–4) = 7–32
78 · 7–4 = 78 ÷ (–4) = 7–2
78 · 7–4 = 78 + (–4) = 74
78 · 7–4 = 78 - (–4) = 712

Answer 1

Use the rule a^m · a^n = a^(m+n). Here m = 8 and n = −4, so

7^8 · 7^(−4) = 7^(8 + (−4)) = 7^4 = 2401.

Thus the third option (7^8 · 7^(−4) = 7^8 + (−4) = 7^4) is correct.