which expression is equivalent to $sqrt3{x^{5}y}$?\n$x^{\frac{5}{3}}y$\n$x^{\frac{5}{3}}y^{\frac{1}{3}}$\n$x^…
which expression is equivalent to $sqrt3{x^{5}y}$?\n$x^{\frac{5}{3}}y$\n$x^{\frac{5}{3}}y^{\frac{1}{3}}$\n$x^{\frac{3}{5}}y$\n$x^{\frac{3}{5}}y^{3}$
Answer
Explanation:
Step1: Use radical - exponent rule
Recall that $\sqrt[n]{a}=a^{\frac{1}{n}}$. So, $\sqrt[3]{x^{5}y}=(x^{5}y)^{\frac{1}{3}}$.
Step2: Apply power - of - a product rule
The power - of - a product rule $(ab)^n=a^n b^n$. Then $(x^{5}y)^{\frac{1}{3}}=x^{5\times\frac{1}{3}}y^{\frac{1}{3}}=x^{\frac{5}{3}}y^{\frac{1}{3}}$.
Answer:
$x^{\frac{5}{3}}y^{\frac{1}{3}}$ (the second option)