Questions: Write the following in simplified radical form. √4(w^11) Assume that the variable represents a positive real number.

Solution Steps

We start with the given expression: \[ \sqrt[4]{w^{11}} \]

To simplify the radical expression, we divide the exponent by the index of the radical. Here, the exponent is 11 and the index is 4.

\[ \sqrt[4]{w^{11}} = w^{\frac{11}{4}} \]

We can separate the exponent into an integer part and a fractional part: \[ w^{\frac{11}{4}} = w^{2 + \frac{3}{4}} = w^2 \cdot w^{\frac{3}{4}} \]

Rewrite the expression using the radical form for the fractional exponent: \[ w^2 \cdot w^{\frac{3}{4}} = w^2 \cdot \sqrt[4]{w^3} \]

Final Answer