Answer:
Option (A)
Step-by-step explanation:
The given expression is,
[tex](5^{-2}\times 4^{-4})^{-2}[/tex]
Since [tex]x^{-1}=\frac{1}{x}[/tex] and [tex]\frac{1}{x^{-1}}=x[/tex]
[tex]5^{2}=\frac{1}{5^{-2}}[/tex]
[tex]4^{2}=\frac{1}{4^{-2}}[/tex]
Therefore, [tex](5^{-2}\times 4^{-4})^{-2}=\frac{1}{(5^{-2}\times 4^{-4})^{2}}[/tex]
[tex]=\frac{1}{(5^{-2})^2\times (4^{-4})^2}[/tex]
[tex]=\frac{1}{5^{-4}\times 4^{-8}}[/tex]
[tex]=\frac{1}{5^{-4}}\times \frac{1}{4^{-8}}[/tex]
[tex]=5^{4}\times 4^{8}[/tex]
Option (A) will be the answer.
