Question

Question 180(iii)

Simplify

${\left(\frac{4}{13}\right)}^4\times {\left(\frac{13}{7}\right)}^2\times {\left(\frac{7}{4}\right)}^3$

Answer 1

${\left(\frac{4}{13}\right)}^4\times {\left(\frac{13}{7}\right)}^2\times {\left(\frac{7}{4}\right)}^3=\frac{(4{)}^4}{(13{)}^4}\times \frac{(13{)}^2}{(7{)}^2}\times \frac{(7{)}^3}{(4{)}^3}=(4{)}^4\times (4{)}^{-3}\times (13{)}^2\times (13{)}^{-4}\times (7{)}^3\times (7{)}^{-2}[\because a^{-m}=\frac{1}{a^m}]=(4{)}^{4-3}\times (13{)}^{2-4}\times \left(7{)}^{3-2}\right[\because a^m\times a^n=a^{m-n}]=(4{)}^1\times (13{)}^{-2}\times (7{)}^1=4\times \frac{1}{169}\times 7[\because a^{-m}=\frac{1}{a^m}]=\frac{28}{169}$