Question

^{reciprocal of 1 by 2 the whole raised to -2 divided by 2 by 3 the whole raised to -3}

Answer 1

$$\begin{gathered} \frac{{\left(1/2\right)}^{-2}}{{\left(2/3\right)}^{-3}} \\ =\frac{2^2}{{\left(3/2\right)}^3}\left[\mathrm{as},{\mathrm{a}}^{-\mathrm{m}}=\frac{1}{{\mathrm{a}}^{\mathrm{m}}}\right] \\ =\frac{4}{27/8} \\ =\frac{4}{1}\times \frac{8}{27} \\ =\frac{32}{27} \\ \mathrm{Now},\mathrm{reciprocal}\mathrm{of}\frac{{\left(1/2\right)}^{-2}}{{\left(2/3\right)}^{-3}}=\mathrm{reciprocal}\mathrm{of}=\frac{27}{32} \end{gathered}$$