Calculate (5×7)³: Evaluating a Cubed Expression

The problem requires us to simplify the expression $(5 \times 7)^3$ using the power of a product rule.

The power of a product rule states that for any numbers $a$ and $b$, and any integer $n$, the expression $(a \times b)^n$ can be expanded to $a^n \times b^n$.

Applying this rule to the given expression:

• Identify the values of $a$ and $b$ as $5$ and $7$, respectively.

• Identify $n$ as $3$.

• Substitute using the rule:
  $(5 \times 7)^3 = 5^3 \times 7^3$

The simplified expression is therefore $5^3 \times 7^3$.