1Cademy - Writing $$t^{\frac{1}{2}}$$, $$m^{\frac{1}{3}}$$, and $$r^{\frac{1}{4}}$$ as Radical Expressions

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

Example

Writing $t^{\frac{1}{2}}$ , $m^{\frac{1}{3}}$ , and $r^{\frac{1}{4}}$ as Radical Expressions

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

ⓐ $t^{\frac{1}{2}} = \sqrt{t}$ : The denominator of the fractional exponent is $2$ , which becomes the index of the radical. Since an index of $2$ represents a square root, it is omitted by convention, giving $\sqrt{t}$ .