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

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Answer 1 · 2016-11-21T14:58:55

The answer is $16 a^{6} b^{24} c^{12}$ $16a^6b^24c^12$

The rule is :

${(a^{n})}^{m} = a^{n \times m}$ $(a^n)^m = a^(nxxm)$

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 :

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

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

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

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

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

How do you simplify (2a b ^ { 4} c ^ { 2} ) ^ { 6}(2ab4c2)6(2a b ^ { 4} c ^ { 2} ) ^ { 6}?