Answer:
OPTION B - 25
Step-by-step explanation:
We know that:
[tex]$ (a^x)^y = a^{x . y} $[/tex]
[tex]$ \frac{a^x}{a^y} = a^{x - y} $[/tex]
[tex]$ a^x . a^y = a^{x + y} $[/tex]
The given problem uses these results to arrive at the answer.
[tex]$ (5^2)^{-3} = 5^{2 . (-3)} = 5^{-6} $[/tex]
Now, [tex]$ 5^{-6 + 4} = 5^{-2} $[/tex]
Now, [tex]$ \frac{5^{-2}}{5^{-4}} = 5^{-2 -(-4)} = 5^{(-2 + 4)} = 5^2 $[/tex]
⇒ 5² = 25.
∴ The answer is 25. (Option B)
