Question

Identify the greatest number among the given options.

• A. $\frac{1}{2^{-3}}$
• B. $2^{-3}$
• C. $\frac{1}{3^{-2}}$
• D. $3^{-2}$

Answer 1

The correct option is C $\frac{1}{3^{-2}}$

We know, $a^{-m}=\frac{1}{a^m}$
$\therefore \frac{1}{2^{-3}}=\frac{1}{\frac{1}{2^3}}=2^3=8.$

$2^{-3}=\frac{1}{2^3}=\frac{1}{8}=0.125$

$\frac{1}{3^{-2}}=3^2=9$

$3^{-2}=\frac{1}{3^2}=\frac{1}{9}=0.111$

Hence, $\frac{1}{3^{-2}}$ is the greatest of all the given options.