Divisors in powers and multiplications

Fill in the blank:

\(a\) and \(b\) are positive integers such that \(\hspace{20cm} \)

  • \( a^b\) has exactly 5 positive divisors;
  • \(b^a \) has exactly 7 positive divisors;
  • \( a\times b\) has exactly \(\text{_______} \) positive divisors.
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