Final answer:
The query requires the application of Euler's Theorem involving Euler's totient function for given numbers, raising them to specified powers, and perhaps further operations applying modulo arithmetic.
Step-by-step explanation:
The student appears to be asking for the application of Euler's Theorem to solve a problem involving raising Euler's totient function to a power. The totient function, often denoted as Φ16 and Φ105, is a function that counts the number of integers up to a given integer 'n' that are relatively prime to 'n'. Euler's Theorem states that if 'n' and 'a' are coprime, then aφ(n) ≡ 1 (mod n). The application of this theorem to the problem (Φ16)32 (Φ105)2 involves finding values for the totient functions and then calculating the powers as specified in the problem. However, without the actual question values or more context, it's not possible to provide a specific solution. The totient values for 16 and 105 would need to be calculated first, which involves factoring these numbers into their prime factors, and then applying the totient function. Once these are found, applying the powers and modulo operations as per Euler's Theorem would yield the answer.