Find the prime factors

SageMath, 31 Bytes

N=input()
print N,"=",factor(N)

Test case: 83891573479027823458394579234582347590825792034579235923475902312344444 Outputs:

83891573479027823458394579234582347590825792034579235923475902312344444 = 2^2 * 3^2 * 89395597 * 98966790508447596609239 * 263396636003096040031295425789508274613

Ruby 1.9, 74 70 characters

#!ruby -plrmathn
$_+=?=+$_.to_i.prime_division.map{|a|a[0,a[1]]*?^}*?*

Edits:

• (74 -> 70) Just use the exponent as slice length instead of explicitly checking for exponent > 1

Perl 5.10, 73 88

perl -pe '$_=`factor $_`;s%( \d+)\K\1+%-1-length($&)/length$1%ge;y, -,*^,;s;\D+;=;'

Takes input number from standard input. Will compute factors for multiple inputs if provided.

Counted as a difference to perl -e. 5.10 is needed for the \K regex metacharacter.