Questions: Write the following as a radical expression. x^(5/6)

Transcript text: Write the following as a radical expression. \[ x^{\frac{5}{6}} \]

Solution

Solution Steps

To convert an expression from exponent form to radical form, we use the property that \( x^{\frac{m}{n}} \) is equivalent to the \( n \)-th root of \( x^m \). In this case, \( x^{\frac{5}{6}} \) can be rewritten as the 6th root of \( x^5 \).

Step 1: Convert Exponent Form to Radical Form

The expression \( x^{\frac{5}{6}} \) can be rewritten using the property of exponents that states \( x^{\frac{m}{n}} = \sqrt[n]{x^m} \). Therefore, we have: \[ x^{\frac{5}{6}} = \sqrt[6]{x^5} \]

Step 2: Express the Radical Form

The radical expression can be explicitly written as: \[ \sqrt[6]{x^5} = (x^5)^{\frac{1}{6}} \]