Question

If $a$ and $b$ are positive integers such that $a^b=125,b\ne 1,$ then $(a-b{)}^{a+b-4}$ is equal to:

• A. $16$
• B. $25$
• C. $28$
• D. $30$

Answer 1

The correct option is A $16$

$a^b=125\Rightarrow a^b=5^3\Rightarrow a=5,b=3$
$\therefore {(a-b)}^{a+b-4}={(5-3)}^{5+3-4}=2^4=16$