Subject: how the heck do u do this?

Name: Kristi Peterson

Who is asking: Student
Level: Middle

Question:
We are doing a math problem for extra credit in our science class, and NO ONE can figure it out at this school! the math problem is:

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

20¹⁰⁰⁰ 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., 10²=100, 10³=1000 -- answer = 1 with number of zero's after it the same as the exponent)

20¹⁰⁰⁰ = (2x10)¹⁰⁰⁰ = (2¹⁰⁰⁰)x(10¹⁰⁰⁰)

10¹⁰⁰⁰ = 1 with one thousand zeros after it (a really big number)

Dealing with 2¹⁰⁰⁰ requires the use of logarithms (high school math) - 2¹⁰⁰⁰ is still too big for a calculator If you are in grade 8, good luck understanding the following:

let y = 2¹⁰⁰⁰ then log y = 1000 x (log 2) = 1000 x (0.301029995) = 301.029995 (approximately) thus,

Putting it all together:

Or

Notice that this is only an approximate answer A computer is needed to handle numbers this large and get an exact answer