what is 9 to the power of 999

We can evaluate   999log(9)  = 953.288

This equals about

 (10⁹⁵³)*10^.288 =

10⁹⁵³ * 1.942 =

1.942 x 10⁹⁵³

All in all......a really big number.....1942 followed by 950 zeros.......!!! {more or less}

Thanks Chris,

I am only just getting the hang of these.    

It is a tricky way of finding high powers that the calc cannot find on its own. 

If you can do a calc that the calc cannot do on its own does that kind of make you = 42?

What is 9 to the power of 999 ?

change of basis: 9 to 10

$$b_1^{ e_1 } = b_2^{ e_2 } \quad | \quad \ln() \\ e_1 \cdot \ln{(b_1)} = e_2 \cdot \ln{(b_2)} \\\\ e_2 = e_1 \cdot \dfrac{ \ln{(b_1)} } { \ln{(b_2)} } \\ \boxed{ b_1^{ e_1 } = b_2^{ e_1 \left( \cdot \dfrac{ \ln{(b_1)} } { \ln{(b_2)} } \right) }}\\\\ \small{\text{ $ b_1 = 9 \qquad e_ 1 = 999 \qquad b_2 = 10 $ }} \\\\ \small{\text{ $ 9^{999} = 10^{999 \left( \cdot \dfrac{ \ln{(9)} } { \ln{(10)} } \right) } $ }} \\\\ \small{\text{ $ 9^{999} = 10^{999 \cdot( 0.95424250944 ) } $ }} \\ \small{\text{ $ 9^{999} = 10^{953.288266930} $ }} \\ \small{\text{ $ 9^{999} = 10^{0.288266930}\cdot 10^{953} $ }} \\ \small{\text{ $ 9^{999} = 1.94207916858 \cdot 10^{953} $ }}$$