Question: Simplify. \[ x^{\frac{2}{5}} \cdot x^{\frac{1}{2}} \] Assume that the variable represents a…

Simplify.

\[ x^{\frac{2}{5}} \cdot x^{\frac{1}{2}} \]

Assume that the variable represents a positive real number.

Solution

To simplify the expression \[ \frac{2}{5x} \cdot \frac{1}{x^2} \] first multiply the numerators and the denominators: \[ \frac{2 \cdot 1}{5x \cdot x^2} \] This simplifies to: \[ \frac{2}{5x^3} \] Thus, the simplified expression is \[ \frac{2}{5x^3} \]