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

asked by guest
on Nov 25, 2024 at 9:48 am



You asked:

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

MathBot Answer:

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

\[\begin{aligned}\frac{{\sqrt{\frac{4}{{9}^{2}}}}^{2}}{\sqrt[3]{{27}^{2}}}& = \left(\sqrt{4 \cdot \frac{1}{9^{2}}}\right)^{2} \cdot \frac{1}{\sqrt[3]{27^{2}}}\\& = \left(\sqrt{\frac{4}{81}}\right)^{2} \cdot \frac{1}{\sqrt[3]{27^{2}}}\\& = \left(\frac{2}{9}\right)^{2} \cdot \frac{1}{\sqrt[3]{27^{2}}}\\& = \frac{4}{81} \cdot \frac{1}{\sqrt[3]{27^{2}}}\\& = \frac{4}{81} \cdot \frac{1}{\sqrt[3]{729}}\\& = \frac{4}{81} \cdot \frac{1}{9}\\& = \frac{4}{729}\end{aligned}\]

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