Final answer:
To make 392 a perfect cube, it must be multiplied by 14.
Step-by-step explanation:
To find the smallest number by which 392 must be multiplied so that the product is a perfect cube, we need to factorize 392 and identify its prime factors. The prime factorization of 392 is 2 * 2 * 2 * 7 * 7.
To make the product a perfect cube, we need to make each exponent of the prime factors a multiple of 3. We can do this by multiplying 2 * 7, resulting in a smallest number of 14.
Therefore, 392 must be multiplied by 14 to have a product that is a perfect cube.
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