Question

Simplifique as questões a baixo

Answer 1

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$\sf E_1~\left(\dfrac{2}{3}\right)^2\cdot\left(\dfrac{3}{2}\right)^2\cdot\dfrac{9}{4}\\\sf\dfrac{9}{4}=\dfrac{3^2}{2^2}=\left(\dfrac{3}{2}\right)^2\\\sf\left(\dfrac{2}{3}\right)^2=\left(\dfrac{3}{2}\right)^{-2}\\\sf\left(\dfrac{2}{3}\right)^2\cdot\left(\dfrac{3}{2}\right)^2\cdot\dfrac{9}{4}=\left(\dfrac{3}{2}\right)^{-2}\cdot\left(\dfrac{3}{2}\right)^2\cdot\left(\dfrac{3}{2}\right)^2\\\sf =\left(\dfrac{3}{2}\right)^{-\diagup\!\!\!2+\diagup\!\!\!2+2}=\left(\dfrac{3}{2}\right)^2=\boxed{\sf\dfrac{9}{4}}$

$\sf E_2~\left(\dfrac{4}{7}\right)^{-3}\cdot\left(\dfrac{7}{4}\right)^3\cdot\dfrac{7\cdot7\cdot7}{4\cdot4\cdot4}\\\sf =\left(\dfrac{7}{4}\right)^3\cdot\left(\dfrac{7}{4}\right)^3\cdot\left(\dfrac{7}{4}\right)^3\\\sf =\left(\dfrac{7}{4}\right)^{3+3+3}=\left(\dfrac{7}{4}\right)^9$