Subject: how the heck do u do this? Name: Kristi Peterson
Who is asking: Student
Question: what is 20 to the thousandth power? we have tried and tried to firgure this out, please help us! thank you for your help, Kristi Peterson 8th grader Hi Kristi, 20^{1000} is a really big number (too big for a calculator to handle) so some computation is needed the firts thing to realize is that computation is easy when the base is 10 (e.g., 10^{2}=100, 10^{3}=1000  answer = 1 with number of zero's after it the same as the exponent) 20^{1000} = (2x10)^{1000} = (2^{1000})x(10^{1000}) 10^{1000} = 1 with one thousand zeros after it (a really big number) Dealing with 2^{1000} requires the use of logarithms (high school math)  2^{1000} is still too big for a calculator If you are in grade 8, good luck understanding the following: let y = 2^{1000} then log y = 1000 x (log 2) = 1000 x (0.301029995) = 301.029995 (approximately) thus, = 10^{301} (approximately) = 1 with three humdred and one zeros after it Putting it all together: = (approx. 1 with three hundred and one zeros after it)x(1 with one thousand zeros after it) = approx. 1 with one thousand three hundred and one zeros after it Or = (10^{301})x(10^{1000}) approximately = 10^{301+1000} = 10^{1301} = 1 with one thousand three hundred and one zeros after it Notice that this is only an approximate answer A computer is needed to handle numbers this large and get an exact answer Paul
