# Dividing exponent with same base

There are $$~2^{80}~$$ possibilities to calculate and I want to divide it by $$~2~$$ to process it by two computers at the same time to find the answer maybe sooner.

How can I divide $$~2^{80}~$$ by $$~2~$$?

• Do you mean $\frac{2^{80}}{2} = 2^{80-1} = 2^{79}$? or something else? – mlchristians Jul 16 '19 at 5:07
• @mlchristians yes exactly. – R1w Jul 16 '19 at 5:09
• Well, there you have it. – mlchristians Jul 16 '19 at 5:09
• @mlchristiansThanks. – R1w Jul 16 '19 at 5:09
• $\frac{2^{80}}{100} = \frac{2^{80}}{2^{2}5^{2}} = \frac{2^{78}}{5^{2}}.$ – mlchristians Jul 16 '19 at 8:18

$$\frac {2^{80}}2=\frac{2^{80}}{2^1}=2^{80-1}=2^{79}$$ Having two computers does not make much of a dent.
• $1000 \approx 2^{10}$ so it still doesn't help much. $2^{80}$ is really big. – Ross Millikan Jul 16 '19 at 5:12
• Computing the number is easy. Alpha gives $1208925819614629174706176$ instantly. It will do much larger numbers as well. If you know $2^{10}=1024$ it only takes three more multiplies to get there, which is reasonable to do by hand. Doing that many operations in a computer is hard. If you can do $10^{12}$ per second it will take about $10^{12}$ seconds, which is about $30000$ years. – Ross Millikan Jul 16 '19 at 5:24
• To compute the number you just need some software that works with numbers that do not fit into $64$ bits. Wolfram Alpha does that and is available at www.wolframalpha.com. You can just type in 2^80 and get the result. You can do much larger numbers. The programming language Python switches seamlessly into large integers when required. It does $2^{8000}, which has about$2400\$ digits instantly. There is an add-on package to C that will handle large numbers, but I am not familiar with it. Maple and Mathematica will do this. I suspect there are add-ons for any popular programming language – Ross Millikan Jul 16 '19 at 13:50