Question

Simplify and give reasons ${\left(\frac{4}{7}\right)}^{-5}\times {\left(\frac{7}{4}\right)}^{-7}$

Answer 1

${\left(\frac{4}{7}\right)}^{-5}\times {\left(\frac{7}{4}\right)}^{-7}$

$={\left(\frac{4}{7}\right)}^{-5}\times {\left(\frac{4}{7}\right)}^7$ using $a^{-m}=\frac{1}{a^m}$

$={\left(\frac{4}{7}\right)}^{-5+7}$ using $a^m\times a^n=a^{m+n}$

$=\frac{4^2}{7^2}$ using ${\left(\frac{a}{b}\right)}^m=\frac{a^m}{b^m}$

$=\frac{16}{49}$