Explanation:

Let’s break it down:

- First, let’s find the prime factorization of 175760:

- 175760 ÷ 2 = 87880 ÷ 2 = 43940 ÷ 2 = 21970 ÷ 2 = 10985

- 10985 ÷ 5 = 2197 ÷ 13 = 169 ÷ 13 = 13

So, Prime factorization:

175760 = 24 × 5 × 13³

- For a number to be a perfect cube, all exponents in its prime factorization must be multiples of 3.

- 24: Needs 2 more to make it 26 (since 6 is a multiple of 3).

- 5¹: Needs 2 more to make it 5³.

- 13³: Already a power of 3.

- To make it a perfect cube, multiply by: 2² × 5² = 4 × 25 = 100.

- Option 1: 100

- Option 2: 160 (not a correct adjustment)

- Option 3: 80 (not enough)

- Option 4: 27 (not enough)

Correct Answer: Option 1 - 100