Express each of the following exponential expressions as a rational number. ${(\frac{2}{3})}^{(- 1)} + {(\frac{3}{2})}^{(- 2)}$

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Solution

${(\frac{2}{3})}^{- 1} + {(\frac{3}{2})}^{- 2}$
$\Rightarrow \frac{3}{2} + {(\frac{2}{3})}^{2}$
$\Rightarrow \frac{3}{2} + \frac{4}{9}$
$\Rightarrow \frac{27 + 8}{18} = \frac{35}{18}$ .

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