Calculate (5×3)³: Order of Operations with Cubes

To solve this problem, we'll clarify our understanding and execution as follows:

• Identify the given expression: $(5 \times 3)^3$.

• Apply the relevant formula: the power of a product rule —$(a \times b)^n = a^n \times b^n$.

• Execution: Rewrite $(5 \times 3)^3$ as $5^3 \times 3^3$.

Let's walk through the solution:

Initially, we have the expression $(5 \times 3)^3$. We recognize that by the power of a product rule, this can be rewritten as $5^3 \times 3^3$.

Next, let's verify the choices:
- $5^3 \times 3$ is incorrect as the exponent doesn't apply to both factors.
- $15^3$ represents the base simplified ($5\times3=15$).
- $5^3 \times 3^3$ matches exactly what we derived earlier, making this the correct expression resulting from the power rule.

Therefore, the correct choice is option is "Answers (b) and (c) are correct". This acknowledges that "B" expresses $15^3$, and "C" independently describes the valid expanded expression, both solutions for different cases of interpretations.