What is 8 to the power of 2015

To get an approximate answer, use logs:

x = 8²⁰¹⁵

--->   log(x)  =  log(8²⁰¹⁵)

Since exponents in logs come out as multipliers:

--->   log(x)  =  2015·log(8)  ≈  1819.726

Find the antilog:

--->   x  =  10^1819.726324

--->   x  =  10^{1819 + 0.726324}

--->   x  =  10¹⁸¹⁹ · 10^0.726324

My calculator give me the value of 5.325 for 10^0.726324

So, the answer is approximately 5.325 x 10¹⁸¹⁹

 8 is not that far from 10. So it isn't unlikely that 8²⁰¹⁵ has at least more than 1000 digits. Thus I use Wolfram Alpha to calculate this:

 

8²⁰¹⁵ ≈ 5.33 * 10¹⁸¹⁹.

 

Guess I was right ;)