1. Analyze the Divisor

The number $\(15^k\)$ can be broken down into its prime factors:

$$
\(15^k=(3 \times 5)^k=3^k \times 5^k\)
$$


For $15^k$ to be a divisor of 759,325 , both $3^k$ and $5^k$ must be factors of 759,325 .
2. Check for Divisibility by 3

A quick way to check if a number is divisible by 3 is to sum its digits. If the sum is divisible by 3 , the number is as well.
For 759, 325:

$$
\(7+5+9+3+2+5=31\)
$$


Since 31 is not divisible by 3 , the number 759,325 has no factors of 3 (its prime factorization contains $\(3^0\)$ ).
3. Determine the value of $k$

Since $3^k$ must divide 759,325 and the highest power of 3 that divides 759,325 is $3^0$, we must have:

$$
\(k \leq 0\)
$$

Given that $k$ is a non-negative integer, the only possible value for $k$ is:

$$
\(k=0\)
$$


Let's verify: $\(15^0=1\)$, and 1 is a divisor of any integer. Thus, $\(k=0\)$ is valid.

4. Calculate the Expression

Now we plug $\(k=0\)$ into the requested formula:

$$
\(\begin{aligned}
& 3^k-k^3 \\
& 3^0-0^3 \\
& 1-0=1
\end{aligned}\)
$$


The correct answer is B. 1.