Question 1133646

 in the set {3^5000,4^4000,5^3000,6^2000,7^1000}

rewrite {{{4^4000}}} as {{{(2^2)^4000=2^8000}}}

 {3^5000,2^8000,5^3000,6^2000,7^1000}

compare exponents:

{{{8000>5000>3000>2000>1000}}}

=>{{{4^4000}}} is largest

check:

{{{3^(5000)=4.0389976297871553397* 10^2385}}}-> compare exponents again
{{{4^(4000)=1.73766203193809456 *highlight(10^2408)}}}
{{{5^(3000)=8.12854862555773544*10^2096}}}
{{{6^(2000)=2.0067846354902095384* 10^1556}}}
{{{7^(1000)=1.2532566399657183181* 10^845}}}