Question

If $5^{m+2}$ $\times$ $5^4$ = $5^3$ , then $m$ = .

• A. 0
• B. -1
• C. -4
• D. -3

Answer 1

The correct option is D -3

Note that for a non-zero integer $a$ and integers $m$ and $n$,
$a^m\times a^n=a^{m+n}$
$\therefore 5^{m+2}\times 5^4=5^{m+2+4}=5^{m+6}=5^3$
Since the bases of powers on both sides of the equation are equal, the exponents can be equated.
m + 6 = 3
$\Rightarrow$ m = -3