Most of the denominators are a pain to calculate.
HOWEVER, the first one (A) is reasonable.

A. \(\frac{7}{16 \times 25}=\frac{7}{400}\)

Now, let's check the remaining answer choices....


B. \(\frac{5}{32 \times 5^4}\)
5^4 (which we should memorize before test day) = 625
So, the denominator is already a lot bigger than 400, which means this fraction is definitely LESS THAN \(\frac{7}{400}\)


C. \(\frac{30}{512 \times 5^3}\)
Same scenario here.
5^3 = 125, so the denominator here is (512)(125), which is HUGE.
So, even with 30 as the numerator, this fraction is definitely LESS THAN \(\frac{7}{400}\)


D. \(\frac{5}{4^6 \times 5}\)
4^6 = (4^3)(4^3)
= (64)(64)
= some number BIGGER than 3600
That's already a huge denominator, which means this fraction is definitely LESS THAN \(\frac{7}{400}\)


E. \(\frac{4}{2^{11}\times 5^2}\)

2^11 = 2048
I'll stop right there, since we can already see that this fraction is definitely LESS THAN \(\frac{7}{400}\)

Answer: A