Write the prime decomposition of 252 in index form.

Final answer: The prime decomposition of 252 in index form is 2² × 3² × 7, after breaking it down step by step through division by the smallest possible primes until only prime numbers are left. Explanation: To write the prime decomposition of 252 in index form, we need to break it down into its prime factors and express it as powers of prime numbers. We start by finding the smallest prime number that divides into 252, which is 2. After dividing 252 by 2, we get 126. We continue this process until we are only left with prime numbers. 252 ÷ 2 = 126 126 ÷ 2 = 63 63 is not divisible by 2, but it is divisible by 3, so 63 ÷ 3 = 21 21 ÷ 3 = 7 7 is a prime number and cannot be factored further Thus, we have the prime factors of 252 as 2, 2, 3, 3, and 7. In index form, the prime numbers are written as bases with exponents indicating how many times each prime number is a factor. The prime decomposition in index form is 2² × 3² × 7.