Question

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

Answer 1

We need to simplify

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

$\because a^{-m}=\frac{1}{a^m}\text{and}{\left|\frac{a}{b}\right|}^{-m}=\frac{a^{-m}}{b^{-m}}$

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

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

$=\frac{\frac{1}{4^5}}{\frac{1}{7^5}}\times \frac{\frac{1}{7^7}}{\frac{1}{4^7}}=\frac{7^5}{4^5}\times \frac{4^7}{7^7}$

$=\frac{4^2}{7^2}$

$=\frac{16}{49}$