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