Question

Write the reciprocal of:

(i) ${\left(\frac{2}{3}\right)}^4$
(ii) ${\left(\frac{-3}{5}\right)}^{61}$
(iii) 2⁵
(iv) (−5)⁶

Answer 1

We know that the reciprocal of ${\left(\frac{a}{b}\right)}^m$ is ${\left(\frac{b}{a}\right)}^m$.

(i) Reciprocal of ${\left(\frac{2}{3}\right)}^4$= ${\left(\frac{3}{2}\right)}^4$

(ii) Reciprocal of ${\left(\frac{-3}{5}\right)}^{61}={\left(\frac{-5}{3}\right)}^{61}$

(iii) Reciprocal of 2⁵ = Reciprocal of ${\left(\frac{2}{1}\right)}^5={\left(\frac{1}{2}\right)}^5$

(iv) Reciprocal of (−5)⁶ = Reciprocal of ${\left(\frac{-5}{1}\right)}^6={\left(\frac{-1}{5}\right)}^6$