Question: Rewrite the following radical with a rational exponent. \[ \sqrt[4]{3y} \] \[ \sqrt[4]{3y} =…

Rewrite the following radical with a rational exponent.

\[ \sqrt[4]{3y} \]

\[ \sqrt[4]{3y} = \boxed{\phantom{xxxx}} \text{(Use integers or fractions for any numbers in the expression.)} \]

Solution

To rewrite the radical with a rational exponent, you can use the property that the nth root of a number is the same as that number raised to the power of \( \frac{1}{n} \). The expression given is: \[ \sqrt[4]{3y} \] This can be rewritten using rational exponents as: \[ (3y)^{\frac{1}{4}} \] So, the expression \( \sqrt[4]{3y} \) can be rewritten with a rational exponent as \( (3y)^{\frac{1}{4}} \).