Question

select all the expressions that are equivalent to $5^{-2} \cdot 4^{-2}$.
$20^{4}$ $\frac{1}{20^{2}}$
$\frac{1}{20^{-2}}$ $20^{-2}$

Explanation:

Step1: Simplify original expression

$5^{-2} \cdot 4^{-2} = \frac{1}{5^2} \cdot \frac{1}{4^2} = \frac{1}{25 \cdot 16} = \frac{1}{400}$

Step2: Check each option

Option A: $20^4 = 160000
eq \frac{1}{400}$
Option B: $\frac{1}{20^2} = \frac{1}{400}$ (matches)
Option C: $\frac{1}{20^{-2}} = 20^2 = 400
eq \frac{1}{400}$
Option D: $20^{-2} = \frac{1}{20^2} = \frac{1}{400}$ (matches)

Answer:

B. $\frac{1}{20^2}$, D. $20^{-2}$