Question

select the correct answer.

rewrite the following radical expression in rational exponent form.

\\(\sqrt7{x})^3\\

• \\(x^{\frac{7}{3}}\\)
• \\((\frac{1}{x^3})^7\\)
• \\(\frac{x^3}{x^7}\\)
• \\(x^{\frac{3}{7}}\\)

Explanation:

Convert radical to rational exponent

$$ \sqrt[7]{x} = x^{\frac{1}{7}} $$

Apply the power of a power rule

$$ (\sqrt[7]{x})^3 = (x^{\frac{1}{7}})^3 = x^{\frac{3}{7}} $$

Answer:

• (A) \(x^{\frac{7}{3}}\)
• (B) \((\frac{1}{x^3})^7\)
• (C) \(\frac{x^3}{x^7}\)
• (D) \(x^{\frac{3}{7}}\) (Correct answer)