Question

alguém pode me ajudar a resolver essa questão de simplifição exponencial?

Gabarito: D)

Answer 1

$\dfrac{2a^2x}{3}(a^2x^2)^{-\frac23}=\dfrac{2a^2x}{3}(a^{2\times(-\frac23)}x^{2\times(-\frac23)})=\dfrac{2a^2x}{3}(a^{-\frac43}x^{-\frac43})=\\\\\dfrac{2a^{2-\frac43} x^{1-\frac43}}{3}=\dfrac{2a^\frac23x^{-\frac13}}{3}=\dfrac{2a^\frac23}{3x^{\frac13}}=\dfrac{2\sqrt[3]{a^2}}{3\sqrt[3]{x}}=\dfrac{2\sqrt[3]{a^2}}{3\sqrt[3]{x}}\cdot\dfrac{\sqrt[3]{x^2}}{\sqrt[3]{x^2}}=\\\\\boxed{\dfrac{2\sqrt[3]{a^2x^2}}{3x}}$