$\text{a)}\sqrt[3]{{19}^3}=19$  

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$\text{b)}\sqrt[3]{{\left(-8\right)}^3}=-8$   

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$\text{c)}{\left(\sqrt[3]{21}\right)}^3=21$  

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$\text{d)}{\left(\sqrt[3]{\frac{3}{4}}\right)}^3=\frac{3}{4}$  

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$\text{e)}{\left(\sqrt[3]{5^3}\right)}^3=5^3=125$  

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$\text{f)}{\left(\sqrt[3]{{\left(-\frac{1}{3}\right)}^3}\right)}^3={\left(-\frac{1}{3}\right)}^3=-\frac{1}{27}$  

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$\text{g)}\sqrt[3]{{\left(\sqrt[3]{{\left(-3\right)}^3}\right)}^3}=\sqrt[3]{{\left(-3\right)}^3}=-3$  

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$\text{h)}{\left(\sqrt[3]{{\left(\sqrt[3]{3^3}\right)}^3}\right)}^3={\left(\sqrt[3]{3^3}\right)}^3=3^3=27$