How do you simplify $\frac{(a^{4} b c^{2}) {(3 a^{4} b^{3} c^{2})}^{2}}{{(3 a^{3} b^{3} c^{2})}^{3}}$ $\frac { ( a ^ { 4} b c ^ { 2} ) ( 3a ^ { 4} b ^ { 3} c ^ { 2} ) ^ { 2} } { ( 3a ^ { 3} b ^ { 3} c ^ { 2} ) ^ {3} }$ ?

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How do you simplify $\frac{(a^{4} b c^{2}) {(3 a^{4} b^{3} c^{2})}^{2}}{{(3 a^{3} b^{3} c^{2})}^{3}}$ $\frac { ( a ^ { 4} b c ^ { 2} ) ( 3a ^ { 4} b ^ { 3} c ^ { 2} ) ^ { 2} } { ( 3a ^ { 3} b ^ { 3} c ^ { 2} ) ^ {3} }$ ?

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Answer 1 · 2017-12-09T13:54:04

the simplified form is $\frac{1}{3} \frac{a^{3}}{b^{2}}$ $1/3a^3/b^2$

Explanation:

given $\frac{(a^{4} b c^{2}) {(3 a^{4} b^{3} c^{2})}^{2}}{{(3 a^{3} b^{3} c^{2})}^{3}} \Rightarrow \frac{(a^{4} b c^{2}) (9 a^{8} b^{6} c^{4})}{27 a^{9} b^{9} c^{6}}$ $[(a^4bc^2)(3a^4b^3c^2)^2]/(3a^3b^3c^2)^3rArr[(a^4bc^2)(9a^8b^6c^4)]/(27a^9b^9c^6)$

$\Rightarrow \frac{9 a^{8 + 4} . b^{6 + 1} . c^{4 + 2}}{27 a^{9} b^{9} c^{6}} \Rightarrow \frac{a^{12} . b^{7} c^{6}}{3 a^{9} b^{9} c^{6}} \Rightarrow \frac{1}{3} [a^{12 - 9} . b^{7 - 9} . c^{6 - 6}]$ $rArr[9a^(8+4).b^(6+1).c^(4+2)]/(27a^9b^9c^6)rArr(a^12.b^7c^6)/(3a^9b^9c^6)rArr1/3[a^(12-9).b^(7-9).c^(6-6)]$

$\Rightarrow \frac{1}{3} \frac{a^{3}}{b^{2}}$ $rArr1/3a^3/b^2$

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How do you simplify $\frac{(a^{4} b c^{2}) {(3 a^{4} b^{3} c^{2})}^{2}}{{(3 a^{3} b^{3} c^{2})}^{3}}$ $\frac { ( a ^ { 4} b c ^ { 2} ) ( 3a ^ { 4} b ^ { 3} c ^ { 2} ) ^ { 2} } { ( 3a ^ { 3} b ^ { 3} c ^ { 2} ) ^ {3} }$ ?

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How do you simplify (a4bc2)(3a4b3c2)2(3a3b3c2)3\frac { ( a ^ { 4} b c ^ { 2} ) ( 3a ^ { 4} b ^ { 3} c ^ { 2} ) ^ { 2} } { ( 3a ^ { 3} b ^ { 3} c ^ { 2} ) ^ {3} }?

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How do you simplify $\frac{(a^{4} b c^{2}) {(3 a^{4} b^{3} c^{2})}^{2}}{{(3 a^{3} b^{3} c^{2})}^{3}}$ $\frac { ( a ^ { 4} b c ^ { 2} ) ( 3a ^ { 4} b ^ { 3} c ^ { 2} ) ^ { 2} } { ( 3a ^ { 3} b ^ { 3} c ^ { 2} ) ^ {3} }$ ?