Chapter 7 - Exponents and Exponential Functions - 7-1 Zero and Negative Exponents - Practice and Problem-Solving Exercises - Page 423: 63

Take, for instance, $a=\displaystyle \frac{2}{3}$ $\begin{array}{rllrllrll} a^{-1} & =\dfrac{1}{a^{1}} & & a^{-2} & =\dfrac{1}{a^{2}} & & a^{-3} & =\dfrac{1}{a^{3}}\\\\ & =\dfrac{1}{\dfrac{2}{3}} & & & =\dfrac{1}{(\dfrac{2}{3})^{2}} & & & =\dfrac{1}{(\dfrac{2}{3})^{3}}\\\\ & =\dfrac{3}{2} & & & =\dfrac{1}{\dfrac{2^{2}}{3^{2}}} & & & =\dfrac{1}{\dfrac{2^{3}}{3^{3}}}\\\\ & & & & =\dfrac{3^{2}}{2^{2}} & & & =\dfrac{3^{3}}{2^{3}}\\\\ & & & & =\dfrac{9}{4} & & & =\dfrac{27}{8} \end{array}$

Given above