Question

Express each of the following rational numbers with a negative exponent:
(i) ${\left(\frac{1}{4}\right)}^3$
(ii) $3^5$
(iii) ${\left(\frac{3}{5}\right)}^4$
(iv) ${\left\{{\left(\frac{3}{2}\right)}^4\right\}}^{-3}$
(v) ${\left\{{\left(\frac{7}{3}\right)}^4\right\}}^{-3}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right). \\ {\left(\frac{1}{4}\right)}^3 \\ ={\left(\frac{4}{1}\right)}^{-3}\left[\because {\mathrm{a}}^{-\mathrm{n}}=\frac{1}{{\mathrm{a}}^{\mathrm{n}}}\right] \\ \left(\mathrm{ii}\right). \\ {\left(3\right)}^5 \\ ={\left(\frac{1}{3}\right)}^{-5}\left[\because {\mathrm{a}}^{-\mathrm{n}}=\frac{1}{{\mathrm{a}}^{\mathrm{n}}}\right] \\ \left(\mathrm{iii}\right). \\ {\left(\frac{3}{5}\right)}^4 \\ ={\left(\frac{5}{3}\right)}^{-4}\left[\because {\mathrm{a}}^{-\mathrm{n}}=\frac{1}{{\mathrm{a}}^{\mathrm{n}}}\right] \\ \left(\mathrm{iv}\right). \\ {\left\{{\left(\frac{3}{2}\right)}^4\right\}}^{-3} \\ ={\left(\frac{3}{2}\right)}^{-12}\left[\because {\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{mn}}\right] \\ \left(\mathrm{v}\right). \\ {\left\{{\left(\frac{7}{3}\right)}^4\right\}}^{-3} \\ ={\left(\frac{7}{3}\right)}^{-12}\left[\because {\left({\mathrm{a}}^{\mathrm{m}}\right)}^{\mathrm{n}}={\mathrm{a}}^{\mathrm{mn}}\right] \end{gathered}$$