# Express each of the following rational numbers with a negative exponent:

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) $\left\{\left(\frac{7}{3}\right)^{4}\right\}^{-3}$

Solution:

(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).

$\left\{\left(\frac{7}{3}\right)^{4}\right\}^{-3}$

$=\left(\frac{7}{3}\right)^{-12} \quad\left[\because\left(\mathrm{a}^{\mathrm{m}}\right)^{\mathrm{n}}=\mathrm{a}^{\mathrm{mn}}\right]$