Question

which expression is equivalent to \\(\sqrt3{x^5 y}\\)?

• \\(x^{\frac{5}{3}} y\\)
• \\(x^{\frac{5}{3}} y^{\frac{1}{3}}\\)
• \\(x^{\frac{3}{5}} y\\)
• \\(x^{\frac{3}{5}} y^3\\)

Explanation:

Apply radical to exponent rule

Using the Radical to Exponential Form knowledge point

$$ \sqrt[n]{a} = a^{\frac{1}{n}} $$

Rewrite the given expression

Using the Radical to Exponential Form knowledge point

$$ \sqrt[3]{x^5 y} = (x^5 y)^{\frac{1}{3}} $$

Distribute the exponent

Using the Rational Exponents knowledge point

$$ (x^5 y)^{\frac{1}{3}} = (x^5)^{\frac{1}{3}} \cdot y^{\frac{1}{3}} = x^{\frac{5}{3}} y^{\frac{1}{3}} $$

Answer:

• (A) \(x^{\frac{5}{3}}y\)
• (B) \(x^{\frac{5}{3}}y^{\frac{1}{3}}\) (Correct answer)
• (C) \(x^{\frac{3}{5}}y\)
• (D) \(x^{\frac{3}{5}}y^3\)