Addition, Multiplication, Exponentiation. What's next?

Algebra Level 2

Note that 9 + 9 + 9 + 9 + ⋯ + 9 ⏟ Number 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 × ⋯ × 9 ⏟ Number of 9’s = 9 = 9 9 . \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 + ⋯ + 9 ⏟ Number of 9’s = N = 9 9 \underbrace{9 + 9 + 9 + 9 + \cdots + 9 }_{\text{Number of 9's }= N} = 9^ 9 , what is N N ?

9 10 9^{10} 9 7 9^7 9 9 9^9 9 8 9^8

Pi Han Goh by Pi Han Goh , 30, Malaysia

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2 solutions

Rahil Sehgal
Mar 21, 2017

3 Helpful 0 Interesting 0 Brilliant 0 Confused

The hardest part is reading sideways lol. I did it the same way.

Peter van der Linden - 4 years, 2 months ago
Viki Zeta
Mar 22, 2017

9 + 9 + 9 + … + 9 = 9 9 9 x = 9 9 x = 9 8 9 + 9 + 9 + \ldots + 9 = 9^{9} \\ 9x = 9^9 \\ x = 9^8

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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