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 is given by $(a \times b)^n = a^n \times b^n$.

• 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 "B+C are correct". This acknowledges that "B" expresses $15^3$, and "C" independently describes the valid expanded expression, both right solutions for different cases of interpretations.