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} $

To do:

We have to express the given rational numbers with negative exponents.

Solution:

We know that,

$\frac{1}{a^m}=a^{-m}$ 

$a^{m}=(\frac{1}{a})^{-m}$ 

$(\frac{a}{b})^m=(\frac{b}{a})^{-m}$

Therefore,

(i) $(\frac{1}{4})^{3}=(\frac{4}{1})^{-3}$

$=(4)^{-3}$

(ii) $(3)^{5}=(\frac{1}{3})^{-5}$

(iii) $(\frac{3}{5})^4=(\frac{5}{3})^{-4}$

(iv) $((\frac{3}{2})^{4})^{-3}=(\frac{3}{2})^{4\times(-3)}$

$=(\frac{3}{2})^{-12}$

(v) $((\frac{7}{3})^{4})^{-3}=(\frac{7}{3})^{4\times(-3)}$

$=(\frac{7}{3})^{-12}$

(v) $((\frac{7}{3})^{4})^{-3}=(\frac{7}{3})^{4\times(-3)}$

$=(\frac{7}{3})^{-12}$

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Updated on: 10-Oct-2022

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