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