In how many ways can the expression $a^{5} b^{2} c^{2}$ be rewritten as a product without exponents? The number of ways $a^{5} b^{2} c^{2}$ can be written without exponents is $\square$.

Step 1 ：The expression \(a^{5} b^{2} c^{2}\) can be rewritten as a product without exponents by expanding the exponents. This means that we will have 5 'a's, 2 'b's and 2 'c's.

Step 2 ：We need to find the number of ways these 9 elements can be arranged. This is a permutation problem with repetition.

Step 3 ：The formula for permutations with repetition is \(\frac{n!}{n1! * n2! * ... * nk!}\) where n is the total number of items and n1, n2, ..., nk are the number of times each distinct item is repeated.

Step 4 ：In this case, n = 9 (total number of 'a's, 'b's and 'c's), n1 = 5 (number of 'a's), n2 = 2 (number of 'b's) and n3 = 2 (number of 'c's).

Step 5 ：We can use this formula to calculate the number of ways the expression can be rewritten as a product without exponents.

Step 6 ：Final Answer: The number of ways \(a^{5} b^{2} c^{2}\) can be written without exponents is \(\boxed{756}\).