Question

$( {a}^{3}.b)^{2} .( {a}^{ - 3} ) {}^{2} \div (b {}^{ - 2} \div a {}^{3} ) {}^{2} =$
$= (a.b) {}^{6}$ é uma igualdade? verifique pra mim. mayday...já tentei várias vezes, mas com as letras me embaraço todo :(​

Answer 1

$( {a}^{3}.b)^{2} .( {a}^{ - 3} )^{2} \div (b ^{ - 2} \div a^{3} )^{2} = (a.b) {}^{6} \\\\\\( {a}^{3~.~2}~.~b^2)~.~\left(\frac{1}{a^3}\right)^2~\div~\left(\frac{\frac{1}{b^2}}{a^3}\right)^2=(a.b)^6\\\\\\( {a}^{6}.~b^2)~.~\left(\frac{1}{a^{3.2}}\right)~\div~\left(\frac{\frac{1}{b^2.2}}{a^{3.2}}\right)=(a.b)^6\\\\\\( {a}^{6}.~b^2)~.~\left(\frac{1}{a^{6}}\right)~\div~\left(\frac{\frac{1}{b^4}}{a^{6}}\right)=(a.b)^6$

$\left(\frac{ {a}^{6}.~b^2}{a^{6}}\right)~\div~\left(\frac{1}{a^{6}.b^4}\right)=(a.b)^6\\\\\\b^2~\div~\left(\frac{1}{a^{6}.b^4}\right)=(a.b)^6\\\\\\\left(\frac{b^2}{\frac{1}{a^{6}.b^4}}\right)=(a.b)^6\\\\\\\left(b^2.(a^{6}.b^4)\right)=(a.b)^6\\\\\\(a^{6}.b^{4+2})=(a.b)^6\\\\\\(a^{6}.b^{6})=(a.b)^6\\\\\\(a.b)^6=(a.b)^6$

Resposta: Sim, a igualdade está correta