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Simplify:
$ \left(4^{-1}+3^{-1}+6^{-2}\right)^{-1} $
Given:
\( \left(4^{-1}+3^{-1}+6^{-2}\right)^{-1} \)To do:
We have to simplify \( \left(4^{-1}+3^{-1}+6^{-2}\right)^{-1} \).
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,
$(4^{-1}+3^{-1}+6^{-2})^{-1}=(\frac{1}{4}+\frac{1}{3}+\frac{1}{6^2})^{-1}$
$=(\frac{1}{4}+\frac{1}{3}+\frac{1}{36})^{-1}$
$=(\frac{9+12+1}{36})^{-1}$
$=(\frac{22}{36})^{-1}$
$=(\frac{11}{18})^{-1}$
$=\frac{18}{11}$
Hence, $(4^{-1}+3^{-1}+6^{-2})^{-1}=\frac{18}{11}$.
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