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 $N$ ?