If $m$ is the cube root of $n$ , then $n$ is

m^{3}

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\sqrt{m}

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m^{\frac{1}{3}}

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\frac{m}{3}

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Solution

The correct option is A $m^{3}$
Given $m$ is the cube root of $n$ .
$\Rightarrow m = \sqrt[3]{n}$
$\Rightarrow m = n^{\frac{1}{3}}$ [Since, $\sqrt[3]{x} = x^{\frac{1}{3}}$ ]
Cube on both sides, we get
$\Rightarrow m^{3} = (n^{\frac{1}{3}})^{3}$
$\Rightarrow m^{3} = (n^{\frac{1}{3} \times 3})$
$\Rightarrow m^{3} = n$
$∴ n = m^{3}$

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