How do you simplify $\frac{{(3 a b)}^{2} {(4 a^{3} b^{4})}^{3}}{{(6 a^{2} b)}^{4}}$ $\frac{(3ab)^2(4a^3b^4)^3}{(6a^2b)^4}$ ?

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Answer 1 · 2014-11-02T15:14:47

$\frac{{(3 a b)}^{2} {(4 a^{3} b^{4})}^{3}}{{(6 a^{2} b)}^{4}}$ ${(3ab)^2(4a^3b^4)^3}/{(6a^2b)^4}$

since $4 = 2^{2}$ $4=2^2$ and $6 = 3 \cdot 2$ $6=3cdot2$ ,

$= \frac{{(3 a b)}^{2} {(2^{2} a^{3} b^{4})}^{3}}{{(3 \cdot 2 a^{2} b)}^{4}}$ $={(3ab)^2(2^2a^3b^4)^3}/{(3cdot2a^2b)^4}$

by distributing the powers,

$= \frac{3^{2} a^{2} b^{2} \cdot 2^{6} a^{9} b^{12}}{3^{4} 2^{4} a^{8} b^{4}}$ $={3^2a^2b^2 cdot 2^6a^9b^{12}}/{3^4 2^4a^8b^4}$

by collecting like factors,

$= \frac{3^{2} 2^{6} a^{11} b^{14}}{3^{4} 2^{4} a^{8} b^{4}}$ $={3^2 2^6a^{11}b^{14}}/{3^4 2^4a^8b^4}$

By cancelling out $3^{2}$ $3^2$ , $2^{4}$ $2^4$ , $a^{8}$ $a^8$ , and $b^{4}$ $b^4$ ,

$= \frac{2^{2} a^{3} b^{10}}{3} = \frac{4}{3} a^{3} b^{10}$ $={2^2a^3b^{10}}/{3}=4/3a^3b^{10}$

I hope that this was helpful.

How do you simplify (3ab)2(4a3b4)3(6a2b)4\frac{(3ab)^2(4a^3b^4)^3}{(6a^2b)^4}?