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Simplify:
\( \frac{1}{6^{-2}}\left[\left(\frac{2}{3}\right)^{2}\right]^{-1} \times\left(\frac{4}{9}\right) \times 7^{0} \)
Given:
\( \frac{1}{6^{-2}}\left[\left(\frac{2}{3}\right)^{2}\right]^{-1} \times\left(\frac{4}{9}\right) \times 7^{0} \)
To do:
We have to simplify the given expression.
Solution:
We know that,
$(a^{m})^{n}=a^{m n}$
$a^{m} \times a^{n}=a^{m+n}$
$a^{m} \div a^{n}=a^{m-n}$
$a^{0}=1$
Therefore,
$\frac{1}{6^{-2}}[(\frac{2}{3})^{2}]^{-1} \times(\frac{4}{9}) \times 7^{0}=6^2[\frac{4}{9}]^{-1}\times(\frac{4}{9}) \times 1$
$=36\times\frac{9}{4}\times\frac{4}{9}$
$=36$
Hence, $\frac{1}{6^{-2}}[(\frac{2}{3})^{2}]^{-1} \times(\frac{4}{9}) \times 7^{0}=36$.
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