To find the remainder when [(919) ^ 6] is divided by 8, we can apply the concept of modular arithmetic.

Modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value called the modulus. In this case, we are working with a modulus of 8.

To find the remainder, we need to find the value of [(919) ^ 6] modulo 8.

Step 1: Simplify the base
We can start by simplifying the base, which is 919.

919 ≡ 7 (mod 8)

This means that 919 is congruent to 7 modulo 8.

Step 2: Apply the exponent
Next, we can apply the exponent of 6 to the simplified base.

(919) ^ 6 ≡ (7) ^ 6 (mod 8)

Step 3: Calculate the exponent modulo 8
To simplify the exponent, we can find the remainder when 6 is divided by 8.

6 ≡ 6 (mod 8)

Since 6 is already less than 8, the remainder is simply 6.

Step 4: Calculate the base raised to the simplified exponent modulo 8
Now, we can calculate (7) ^ 6 modulo 8.

(7) ^ 6 ≡ (7 ^ 6) (mod 8)

To find the value of (7 ^ 6) modulo 8, we can expand the exponent and evaluate each term modulo 8.

(7 ^ 6) ≡ (7 * 7 * 7 * 7 * 7 * 7) (mod 8)

Since we are working with modulo 8, we only need to consider the remainder when each term is divided by 8.

(7 * 7 * 7 * 7 * 7 * 7) ≡ (49 * 49 * 49) ≡ (1 * 1 * 1) ≡ 1 (mod 8)

Therefore, (7 ^ 6) modulo 8 is equal to 1.

Step 5: Calculate the remainder
Finally, we can substitute the simplified exponent back into the equation to find the remainder.

(919) ^ 6 ≡ (7) ^ 6 ≡ 1 (mod 8)

The remainder when [(919) ^ 6] is divided by 8 is 1.

Therefore, the correct answer is option B) 1.