\sqrt{\left(\frac{4}{9^2}\right)}^2\div \sqrt[3]{27^2}

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on Nov 25, 2024 at 9:48 am



You asked:

Evaluate the expression: 49222723\frac{{\sqrt{\frac{4}{{9}^{2}}}}^{2}}{\sqrt[3]{{27}^{2}}}

MathBot Answer:

49222723=4729=0.005486968449931412894375857338820301783264746227709190672153635116598079561042524‾\frac{{\sqrt{\frac{4}{{9}^{2}}}}^{2}}{\sqrt[3]{{27}^{2}}} = \frac{4}{729} = 0.\overline{005486968449931412894375857338820301783264746227709190672153635116598079561042524}

49222723=(4⋅192)2⋅12723=(481)2⋅12723=(29)2⋅12723=481⋅12723=481⋅17293=481⋅19=4729\begin{aligned}\frac{{\sqrt{\frac{4}{{9}^{2}}}}^{2}}{\sqrt[3]{{27}^{2}}}&=\left(\sqrt{4 \cdot \frac{1}{9^{2}}}\right)^{2} \cdot \frac{1}{\sqrt[3]{27^{2}}}\\&=\left(\sqrt{\frac{4}{81}}\right)^{2} \cdot \frac{1}{\sqrt[3]{27^{2}}}\\&=\left(\frac{2}{9}\right)^{2} \cdot \frac{1}{\sqrt[3]{27^{2}}}\\&=\frac{4}{81} \cdot \frac{1}{\sqrt[3]{27^{2}}}\\&=\frac{4}{81} \cdot \frac{1}{\sqrt[3]{729}}\\&=\frac{4}{81} \cdot \frac{1}{9}\\&=\frac{4}{729}\end{aligned}

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