Question

select the correct answer.

which expression is equivalent to \\(y^{\frac{2}{5}}\\), if \\(y \
eq 0\\)?

\\(\bigcirc \sqrt5{2y}\\)
\\(\bigcirc \sqrt5{y^2}\\)
\\(\bigcirc \sqrt{y^5}\\)
\\(\bigcirc 2\sqrt5{y}\\)

Explanation:

Identify the given expression and target form

$$ y^{\frac{2}{5}},\quad y eq 0 $$

Apply the definition of rational exponents

$$ a^{\frac{m}{n}} = \sqrt[n]{a^m} $$

Convert the expression to radical form

$$ y^{\frac{2}{5}} = \sqrt[5]{y^2} $$

Answer:

• (A) \(\sqrt[5]{2y}\)
• (B) \(\sqrt[5]{y^2}\) (Correct answer)
• (C) \(\sqrt{y^5}\)
• (D) \(2\sqrt[5]{y}\)