Solve (4/35)^4: Evaluating a Compound Fraction to the Fourth Power

To simplify the expression $\left(\frac{4}{5 \times 7}\right)^4$, we will apply the rule of exponents for fractions, which states that $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$.

Step 1: Identify the components of the fraction.
The fraction is $\frac{4}{5 \times 7}$.

Step 2: Apply the exponent to both the numerator and the denominator separately.
The numerator is 4, and the calculation is $4^4$.
The denominator is $5 \times 7$, and the calculation is $(5 \times 7)^4$.

Step 3: Write the expression with the exponents.
The simplified expression becomes $\frac{4^4}{(5 \times 7)^4}$.

Therefore, the correct expression is $\frac{4^4}{(5 \times 7)^4}$, which corresponds to choice 1.