Question

√(1/2)³×-²=(1/2)-⁴×.2-×+⁴, alguém sabe me explicar?
​

Answer 1

$\large\boxed{\begin{array}{l}\underline{\sf Produto\,de\,bases\,iguais}\\\rm a^m\cdot a^n=a^{m+n}\\\underline{\sf Pot\hat encia\,de\,expoente\,negativo}\\\rm \bigg(\dfrac{a}{b}\bigg)^{-m}=\bigg(\dfrac{b}{a}\bigg)^m\\\underline{\sf pot\hat encia\,de\,uma\,pot\hat encia}\\\rm (a^m)^n=a^{m\cdot n}\\\underline{\sf Pot\hat encia\,de\,expoente\,fracion\acute ario}\\\rm \sqrt[\rm n]{\rm a^m}=a^{\frac{m}{n}}\end{array}}$

$\large\boxed{\begin{array}{l}\rm\sqrt{\bigg(\dfrac{1}{2}\bigg)^{3x-2}}=\bigg(\dfrac{1}{2}\bigg)^{-4x}\cdot2^{-x+4}\\\\\rm\bigg(\dfrac{1}{2}\bigg)^{\frac{3x-2}{2}}=\bigg(\dfrac{1}{2}\bigg)^{-4x}\cdot 2^{-x+4}\\\\\rm (2^{-1})^{\frac{3x-2}{2}}=({2^{-1}})^{-4x}\cdot2^{-x+4}\\\rm 2^{\frac{-3x+2}{2}}=2^{4x}\cdot2^{-x+4}\\\rm 2^{\frac{-3x+2}{2}}=2^{4x-x+4}\\\rm 2^{\frac{-3x+2}{2}}=2^{3x+4}\end{array}}$

$\large\boxed{\begin{array}{l}\rm\dfrac{-3x+2}{2}=3x+4\\\\\rm 2\cdot(3x+4)=-3x+2\\\rm 6x+8=-3x+2\\\rm 6x+3x=2-8\\\rm 9x=-6\\\rm x=-\dfrac{6\div3}{9\div3}\\\\\rm x=-\dfrac{2}{3}\end{array}}$