Final answer:
Upon calculating and simplifying the product of 7/27 × 5/14 × 9/25, the correct answer is 1/30, which does not match any of the provided multiple-choice options. Therefore, none of the options is correct.
Step-by-step explanation:
The multiplication of fractions involves multiplying the numerators together and the denominators together. In the question provided, we are asked to multiply 7/27 × 5/14 × 9/25 and simplify the result.
Performing the multiplication gives us the numerator of 7 × 5 × 9 and the denominator of 27 × 14 × 25. Simplifying these numbers, we get 315 for the numerator and 9450 for the denominator. This fraction can be simplified further by dividing both the numerator and the denominator by the greatest common divisor, which is 315. This results in a simplified fraction of 1/30.
However, after reviewing the multiple-choice answers provided, it appears that none of them match the result of the calculation. There might have been a mistake in the question or in the options provided. So, regrettably, none of the given options (a) 3/10, (b) 1/20, (c) 3/14, or (d) 3/35 match the correct simplified fraction of 1/30.