Final answer:
The prime decomposition of 232 in index form is 2 to the power of 3 multiplied by 29, which is written as 2^3 × 29.
Step-by-step explanation:
To write the prime decomposition of 232 in index form, we first need to find the prime factors of the number. Starting from the smallest prime number, we divide 232 by primes until we are left with 1.
- 232 ÷ 2 = 116
- 116 ÷ 2 = 58
- 58 ÷ 2 = 29
- 29 is a prime number and cannot be divided further.
So, the prime factors of 232 are 2, 2, 2, and 29. To express these in index form, we count the number of times each prime factor appears. For the number 2, it appears three times, and the prime number 29 appears once.
The prime decomposition of 232 in index form is 23 × 29.