Fermat's Little Theorem states that if "p" is a prime number and "a" is any positive integer not divisible by "p," then:

a^(p-1) ≡ 1 (mod p)

In this case, we have "p" as 13 and "a" as 4. Therefore, according to Fermat's theorem:

4^(13-1) ≡ 1 (mod 13)

4¹² ≡ 1 (mod 13)

Now, we can use this result to find 4²²⁵ mod 13 by simplifying the exponent:

4²²⁵ = 4^{(12 * 18 + 9)}

Since 4¹² ≡ 1 (mod 13), we can substitute this into the equation:

4²²⁵ ≡ (4¹²)¹⁸ * 4⁹ ≡ 1¹⁸ * 4⁹ ≡ 4⁹ (mod 13)

Now, need to calculate 4⁹ mod 13:

4⁹ = (4³)³ = 64³ ≡ 1³ ≡ 1 (mod 13)

Therefore, 4²²⁵ mod 13 ≡ 1.

In other words, 4 raised to the power of 225, when taken modulo 13, leaves a remainder of 1.