1Cademy - As a technical analyst standardizing calculation formulas for a logistics database, you are tasked with rationalizing the denominator of the expression $\frac{3}{\sqrt[3]{4x}}$. You recall that the radicand ${}4x$ is equivalent to ${}2^2x$. To complete the factors of 2 and $x$ to the third power, you must multiply both the numerator and the denominator by $\sqrt[3]{2x^n}$. The required value of the exponent $n$ to create a perfect cube for the $x$ variable is ___

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Simplifying $\frac{3}{\sqrt[3]{4x}}$

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As a technical analyst standardizing calculation formulas for a logistics database, you are tasked with rationalizing the denominator of the expression $\frac{3}{\sqrt[3]{4x}}$ . You recall that the radicand ${}4x$ is equivalent to ${}2^2x$ . To complete the factors of 2 and $x$ to the third power, you must multiply both the numerator and the denominator by $\sqrt[3]{2x^n}$ . The required value of the exponent $n$ to create a perfect cube for the $x$ variable is ____.

Updated 2026-09-18

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