Addition, Multiplication, Exponentiation. What's next?

Algebra Level 2

Note that \[ \underbrace{9 + 9 + 9 + 9 + \cdots + 9 }_{\text{Number of 9's }= 9} = 9\times 9 \] and \[ \underbrace{9 \times 9 \times 9 \times 9 \times \cdots \times 9 }_{\text{Number of 9's }= 9} = 9^ 9 . \]

If \( \underbrace{9 + 9 + 9 + 9 + \cdots + 9 }_{\text{Number of 9's }= N} = 9^ 9 \), what is \(N\)?

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