Question: Rewrite following radical with a rational exponent. \[ \sqrt[7]{\frac{x}{5}} \] \[…

Rewrite following radical with a rational exponent.

\[ \sqrt[7]{\frac{x}{5}} \]

\[ \sqrt[7]{\frac{x}{5}} = \boxed{\phantom{xxxx}} \]

Solution

To rewrite the radical expression with a rational exponent, note the 7th root of an expression can be expressed as raising that expression to the power of \( \frac{1}{7} \). The given expression is \[ \sqrt[7]{\frac{x}{5}} \] We can rewrite this as: \[ \left( \frac{x}{5} \right)^{\frac{1}{7}} \] So, the expression with a rational exponent is \[ \left( \frac{x}{5} \right)^{\frac{1}{7}} \]