Chapter R - Section R.8 - nth Roots; Rational Exponents - R.8 Assess Your Understanding - Page 79: 71

$\displaystyle \frac{27\sqrt{2}}{32}$

We simplify: $\displaystyle (\frac{9}{8})^{3/2}=\frac{9^{3/2}}{8^{3/2}}=\frac{(9^{1/2})^3}{((8)^{3})^{1/2}}=\frac{3^3}{(512)^{1/2}}=\frac{27}{(256*2)^{1/2}}=\frac{27}{16\sqrt{2}}=\frac{27\sqrt{2}}{16*2}=\frac{27\sqrt{2}}{32}$