Write the rational exponent as a radical expression. $$ \begin{array}{ll}(E x l) \ ext { a. } 7^{\frac{1}{7}} & ext { b. } 4^{\frac{5}{3}}\end{array} $$

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Write the rational exponent as a radical expression. $$ \begin{array}{ll}(E x l) \ 	ext { a. } 7^{\frac{1}{7}} & 	ext { b. } 4^{\frac{5}{3}}\end{array} $$

UpStudy AI · Accepted Answer

1. For $$ 7^{\frac{1}{7}} $$:
   - The exponent $$\frac{1}{7}$$ indicates a seventh root.
   - Thus, $$ 7^{\frac{1}{7}} = \sqrt[7]{7} $$.

2. For $$ 4^{\frac{5}{3}} $$:
   - The exponent $$\frac{5}{3}$$ can be interpreted as $$4^{\frac{5}{3}} = \left(4^5\right)^{\frac{1}{3}}$$ or equivalently as $$\left( \sqrt[3]{4} \right)^5$$.
   - Therefore, $$ 4^{\frac{5}{3}} = \sqrt[3]{4^5} $$.
$$ 7^{\frac{1}{7}} = \sqrt[7]{7} $$ and $$ 4^{\frac{5}{3}} = \sqrt[3]{4^5} $$.

Write the rational exponent as a radical expression. \( \begin{array}{ll}(E x l) \\ \text { a. } 7^{\frac{1}{7}} & \text { b. } 4^{\frac{5}{3}}\end{array} \)

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