Question

Identify the greatest number among the given options.

• A. $3^{-5}$
• B. ${15}^{-2}$
• C. $4^{-4}$
• D. $7^{-3}$

Answer 1

The correct option is B ${15}^{-2}$

We know that $a^{-m}=\frac{1}{a^m}$ for a non-zero integer $a$ and any integer $m.$
$⟹{15}^{-2}=\frac{1}{{15}^2}=\frac{1}{225}$
$7^{-3}=\frac{1}{7^3}=\frac{1}{343}$
$4^{-4}=\frac{1}{4^4}=\frac{1}{256}$
$3^{-5}=\frac{1}{3^5}=\frac{1}{243}$

$⟹\frac{1}{225}>\frac{1}{243}>\frac{1}{256}>\frac{1}{343}$

Hence, ${15}^{-2}$ is the greatest of the lot.