Chapter 10 - Radical Expressions and Equations - 10-3 Operations with Radial Expressions - Practice and Problem-Solving Exercises - Page 617: 59

a) $x^{n/2}$ b) $x^{(n-1)/2}*\sqrt x$

a) $n=2*y$ where $y$ a real number, so $n$ is even. By this logic, $n/2 = y$. $\sqrt {x^n}$ $\sqrt {x^{2*y}}$ $x^y$ $x^{n/2}$ b) $n=2*y+1$ where $y$ a real number, so $2y$ is even. $2y+1$ is odd, then. By this logic, $(n-1)/2=y$ $\sqrt {x^n}$ $\sqrt {x^{2*y}*x^1}$ $x^y*\sqrt x$ $x^{(n-1)/2}*\sqrt x$