Question

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$\sqrt[3]{a^{2} }m : \sqrt{am}$

Answer 1

$\dfrac{\sqrt[3]{a^2}m}{\sqrt{am}}\\\\\\=\dfrac{\sqrt[3]{a^2}\sqrt{m}^2}{\sqrt{am}}\\\\\\=\dfrac{\sqrt[3]{a^2}\sqrt{m^2}}{\sqrt{am}}\\\\\\=\dfrac{\sqrt[3]{a^2m^2}}{\sqrt{am}}\\\\\\=\dfrac{\sqrt[3]{am}^2}{\sqrt{am}}\\\\\\=\dfrac{(am)^{\frac{2}{3}}}{(am)^\frac{1}{2}}}\\\\\\=(am)^{\frac{2}{3}-\frac{1}{2}}\\\\\\=(am)^{\frac{2\times2-1\times3}{6}}\\\\\\=(am)^{\frac{4-3}{6}}\\\\\\=(am)^{\frac{1}{6}}\\\\\\=\sqrt[6]{am}$