which expression is equivalent to $\frac{sqrt7{x^{2}}}{sqrt5{y^{3}}}$? assume $y\neq0$.\n$left(x^{\frac{2}{7}…

which expression is equivalent to $\frac{sqrt7{x^{2}}}{sqrt5{y^{3}}}$? assume $y\neq0$.\n$left(x^{\frac{2}{7}}\right)left(y^{-\frac{3}{5}}\right)$\n$left(x^{\frac{2}{7}}\right)left(y^{\frac{5}{3}}\right)$\n$left(x^{\frac{2}{7}}\right)left(y^{\frac{3}{5}}\right)$\n$left(x^{\frac{7}{2}}\right)left(y^{-\frac{5}{3}}\right)$

which expression is equivalent to $\frac{sqrt7{x^{2}}}{sqrt5{y^{3}}}$? assume $y\neq0$.\n$left(x^{\frac{2}{7}}\right)left(y^{-\frac{3}{5}}\right)$\n$left(x^{\frac{2}{7}}\right)left(y^{\frac{5}{3}}\right)$\n$left(x^{\frac{2}{7}}\right)left(y^{\frac{3}{5}}\right)$\n$left(x^{\frac{7}{2}}\right)left(y^{-\frac{5}{3}}\right)$

Answer

Explanation:

Step1: Recall the rule of fractional - exponents

The $n$-th root of a number $a$ can be written as $a^{\frac{1}{n}}$. So, $\sqrt[7]{x^{2}}=x^{\frac{2}{7}}$ and $\sqrt[5]{y^{3}} = y^{\frac{3}{5}}$.

Step2: Write the given fraction in terms of exponents

The given expression $\frac{\sqrt[7]{x^{2}}}{\sqrt[5]{y^{3}}}$ can be written as $\frac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}$.

Step3: Use the rule of negative exponents

$\frac{a^{m}}{a^{n}}=a^{m - n}$ and $\frac{a^{m}}{b^{n}}=a^{m}b^{-n}$. So, $\frac{x^{\frac{2}{7}}}{y^{\frac{3}{5}}}=x^{\frac{2}{7}}y^{-\frac{3}{5}}$.

Answer:

$x^{\frac{2}{7}}y^{-\frac{3}{5}}$ (corresponding to the first option in the multiple - choice list)