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

1 Answer
Nov 21, 2016

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

Explanation:

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