Addition, Multiplication, Exponentiation. What's next?

Algebra Level 2

Note that 9+9+9+9++9Number of 9’s =9=9×9 \underbrace{9 + 9 + 9 + 9 + \cdots + 9 }_{\text{Number of 9's }= 9} = 9\times 9 and 9×9×9×9××9Number of 9’s =9=99. \underbrace{9 \times 9 \times 9 \times 9 \times \cdots \times 9 }_{\text{Number of 9's }= 9} = 9^ 9 .

If 9+9+9+9++9Number of 9’s =N=99 \underbrace{9 + 9 + 9 + 9 + \cdots + 9 }_{\text{Number of 9's }= N} = 9^ 9 , what is NN?

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