How do you simplify #(2a b ^ { 4} c ^ { 2} ) ^ { 6}#?

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Answer 1 · 2016-11-21T14:58:55

The answer is #16a^6b^24c^12#

The rule is :

#(a^n)^m = a^(nxxm)#

Which means that :

#P= (a^1xxb^nxxc^mxxd^lxx...)^k#
#=(a^1)^kxx(b^n)^kxx(c^m)^kxx(d^l)^kxx...#
#=a^kxxb^(nxxk)xxc^(mxxk)xxd^(lxxk)xx...#

Using this rule with your example :

#P= (2xxaxxb^4xxc^2)^6#

#=(2^1)^6xx(a^1)^6xx(b^4)^6xx(c^2)^6#

#=2^(1xx6)xxa^(1xx6)xxb^(4xx6)xxc^(2xx6)#

#=2^6xxa^6xxb^24xxc^12#

#=16xxa^6xxb^24xxc^12#