Chapter P, Prerequisites - Section P.4 - Rational Exponents and Radicals - P.4 Exercises - Page 30: 91

(a) $2^{1/2}>2^{1/3}$ (b) $2^{-1/2}<2^{-1/3}$

(a) Since $\displaystyle \frac{1}{2}=0.5>\frac{1}{3}=0.3\bar3$, we know that: $2^{1/2}>2^{1/3}.$ (b) $(\displaystyle \frac{1}{2})^{1/2}=2^{-1/2}$ and $(\displaystyle \frac{1}{2})^{1/3}=2^{-1/3}$ We know that $-\frac{1}{2}=-0.5