Calculate (5×7/71)⁴: Solving a Complex Fraction Power

To solve this problem, we'll follow these steps:

• Step 1: Identify the expression inside the parentheses that needs to be exponentiated.
• Step 2: Apply the power of a fraction rule, $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.
• Step 3: Compute the expression based on this rule.

Now, let's work through each step:

Step 1: The initial expression provided is $\left(\frac{5 \times 7}{71}\right)$. The numerator is $5 \times 7$, and the denominator is $71$.

Step 2: According to the power of a fraction rule, we apply the exponent $4$ to both the numerator and the denominator:

$\left(\frac{5 \times 7}{71}\right)^4 = \frac{(5 \times 7)^4}{71^4}$.

Step 3: Simply ensure the expression aligns with the given multiple-choice options.

The expression is, therefore, $\frac{(5 \times 7)^4}{71^4}$, which matches the choice:

$\frac{\left(5\times7\right)^4}{71^4}$ (Choice 3).

Thus, the solution to the problem is correctly matched as $\frac{\left(5\times7\right)^4}{71^4}$.