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b3c2 ab34 a2bac3\sqrt[4]{b^3c^2\:\sqrt[3]{ab}}\:\sqrt[3]{a^2b\sqrt{ac}}

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Final answer to the exercise

b76c23a(34+16)\sqrt[6]{b^{7}}\sqrt[3]{c^{2}}a^{\left(\frac{3}{4}+\frac{1}{6}\right)}

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