the number of digits in the expansion of 256^39 times 3125^62 is
To find the number of digits in the expansion of a number, we can take the logarithm of that number to the base 10 and add 1.
Let's calculate the number of digits in the expansion of 256^39. First, we can find the value of 256^39 using a calculator or a computer program:
256^39 = 353876272698604037431483676848719128725825574829088002824155080685259420148694282741258630208
Now, we can take the logarithm of 256^39 to the base 10 and add 1:
log10(256^39) = 39 * log10(256) ≈ 39 * 2.40824 ≈ 93.91936
Number of digits = 93.91936 + 1 ≈ 94
Now, let's calculate the number of digits in the expansion of 3125^62:
3125^62 = 7307508186654514591018424163581415098279662714886477594185
log10(3125^62) = 62 * log10(3125) ≈ 62 * 3.49485 ≈ 216.5857
Number of digits = 216.5857 + 1 ≈ 217
Therefore, the number of digits in the expansion of 256^39 times 3125^62 is 94 + 217 = 311.