1Cademy - Writing $$b^{\frac{1}{6}}$$, $$z^{\frac{1}{5}}$$, and $$p^{\frac{1}{4}}$$ as Radical Expressions

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Writing $x^{\frac{1}{2}}$ , $y^{\frac{1}{3}}$ , and $z^{\frac{1}{4}}$ as Radical Expressions

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Writing $b^{\frac{1}{6}}$ , $z^{\frac{1}{5}}$ , and $p^{\frac{1}{4}}$ as Radical Expressions

Convert three additional expressions with rational exponents of the form $\frac{1}{n}$ into radical notation using the equivalence $a^{\frac{1}{n}} = \sqrt[n]{a}$ .

ⓐ $b^{\frac{1}{6}} = \sqrt[6]{b}$ : The denominator of the rational exponent is $6$ , so the base $b$ becomes the radicand of a sixth root: $\sqrt[6]{b}$ .

ⓑ $z^{\frac{1}{5}} = \sqrt[5]{z}$ : The denominator of the exponent is $5$ , so the base $z$ becomes the radicand of a fifth root: $\sqrt[5]{z}$ .

ⓒ $p^{\frac{1}{4}} = \sqrt[4]{p}$ : The denominator of the exponent is $4$ , so the base $p$ becomes the radicand of a fourth root: $\sqrt[4]{p}$ .

This reinforces that the denominator of an exponent of the form $\frac{1}{n}$ directly determines the index of the corresponding radical expression, even for higher-order roots.

Updated 2026-05-01

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OpenStax Intermediate Algebra

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