Question

simplify {(2/3^2)^3}×1/3^-4×3^-1×6^-1

Answer 1

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$\implies$$\large\bf{\underline{\red{VERIFIED✔}}}$

$Given : \\ \\Expression [\{(\frac{2}{3})^2\}^3\times (\frac{1}{3})^{-4}\times 3^{-1}\times (\frac{1}{6})][{(32)2}3×(31)−4×3−1×(61)] \\ \\ To \: find : Simplify \: the \: expression ? \\ \\ Solution : \\ \\ Solving \: the \: expression, \\ \\ [\{(\frac{2}{3})^2\}^3\times (\frac{1}{3})^{-4}\times 3^{-1}\times (\frac{1}{6})][{(32)2}3×(31)−4×3−1×(61)] \\ \\ =[\{(\frac{4}{9})\}^3\times (3)^{4}\times\frac{1}{3} \times (\frac{1}{6})] \\ \\ =[{(94)}3×(3)4×31×(61)] \\ \\ =[\frac{64}{729}\times 81\times\frac{1}{3} \times \frac{1}{6}] \\ \\ =[72964×81×31×61] \\ \\ =\frac{32}{81}=8132 \\ \\ Therefore, [\{(\frac{2}{3})^2\}^3\times (\frac{1}{3})^{-4}\times 3^{-1}\times (\frac{1}{6})] \\ \\ =\frac{32}{81}[{(32)2}3×(31)−4×3−1×(61)] \\ \\ =8132$

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