$$\displaystyle\sqrt[3]{56}$$

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Szeteib

We have to express the given radical expression in simplest radical form:
$$\displaystyle\sqrt[3]{56}$$
We know the laws of exponents,
$$\displaystyle\sqrt[m]{a}={a}^{{{\frac{{{1}}}{{{m}}}}}}$$
$$\displaystyle{\left({a}^{{m}}\right)}^{{n}}={a}^{{{m}\times{n}}}$$
$$\displaystyle{\left({a}{b}\right)}^{{m}}={a}^{{m}}{b}^{{m}}$$
Applying above laws for the given expression, we get
$$\displaystyle\sqrt[3]{56}={\left({56}\right)}^{{\frac{{{1}}}{{{3}}}}}$$
$$\displaystyle={\left({8}\times{7}\right)}^{{\frac{{{1}}}{{{3}}}}}$$
$$\displaystyle={\left({2}\times{2}\times{2}\times{7}\right)}^{{\frac{{{1}}}{{{3}}}}}$$
$$\displaystyle={\left({2}^{{3}}\times{7}\right)}^{{\frac{{{1}}}{{{3}}}}}$$
$$\displaystyle={\left({2}^{{3}}\right)}^{{\frac{{{1}}}{{{3}}}}}{\left({7}\right)}^{{\frac{{1}}{{3}}}}$$
$$\displaystyle={2}\sqrt[3]{7}$$
Hence, simplest form of the radical expression is $$\displaystyle={2}\sqrt[3]{7}$$