Simplify:
$ \left\{\left(\frac{3}{7}\right)^{-2}\right\}^{-3} \div\left(\frac{-9}{49}\right)^{2} $

Given:

\( \left\{\left(\frac{3}{7}\right)^{-2}\right\}^{-3} \div\left(\frac{-9}{49}\right)^{2} \)

To do:

We have to simplify \( \left\{\left(\frac{3}{7}\right)^{-2}\right\}^{-3} \div\left(\frac{-9}{49}\right)^{2} \).

Solution:

We know that,

$a^{-m}=\frac{1}{a^m}$

$a^m \times a^n=a^{m+n}$

$a^{m}\div a^{n}=a^{m-n}$

Therefore,

${(\frac{3}{7})^{-2}}^{-3} \div(\frac{-9}{49})^{2}=[(\frac{7}{3})^2]^{-3} \div (\frac{-3^2}{7^2})^{2}$

$=[(\frac{3}{7})^2]^{3}\times\frac{(-3^2)^2}{(7^2)^2})$

$=(\frac{3}{7})^{3\times2}\times\frac{3^4}{7^4}$

$=(\frac{3}{7})^6\times(\frac{3}{7})^4$

$=(\frac{3}{7})^{6+4}$

$=(\frac{3}{7})^{10}$

Hence, ${(\frac{3}{7})^{-2}}^{-3} \div(\frac{-9}{49})^{2}=(\frac{3}{7})^{10}$.