Most of the answer choices feature products of prime numbers.
This suggests that we may benefit from finding the prime factorization of 17,640

17,640 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 7 = 2³ x 3² x 5 x 7²
So, one answer is A

We can also write:
17,640 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 7
= 2 x 2 x 3 x 3 x 7 x 7 x 2 x 5
= [2 x 3 x 7][2 x 3 x 7] x 2 x 5
= [2 x 3 x 7]² x 10
So, another answer is C

We can also write:
17,640 = 2 x 2 x 2 x 3 x 3 x 5 x 7 x 7
= 8 x 9 x 5 x 7 x 7
= 5 x 7 x 7 x 8 x 9
So, another answer is D

Since there are no 11's in the prime factorization of 17,640, we can ELIMINATE B and E

Answer: A, C, D

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Which of the following expressions is equivalent to 17,640?
Indicate all such expressions.

A. 2^3×3^2×5×7^2
B. 2^3×3^2×7^2×11
C. (2×3×7)^2×10
D. 5×7×7×8×9
E. 7×7×8×9×11

Another way to look at this question is to understand what the question is asking and what help the given options can provide:
Since 17,640 has unit digits ending in 0 , so there must be at least one factor of 2 and 5 to give us the solution.
if we look closely at option B and E , they do not have any 5 as the prime factor so they can be straight away eliminated.
For all the other options if you see they are just a form of expressing the same Prime factorization - 2^3×3^2×5×7^2