Simplify \(\sqrt[3]{81}\) to \(3\sqrt[3]{3}\).
\[\frac{3\sqrt[3]{3}\sqrt[3]{576}}{{64}^{\frac{2}{3}}\times {27}^{\frac{2}{3}}}\]
Simplify \(\sqrt[3]{576}\) to \(4\sqrt[3]{9}\).
\[\frac{3\sqrt[3]{3}\times 4\sqrt[3]{9}}{{64}^{\frac{2}{3}}\times {27}^{\frac{2}{3}}}\]
Rewrite \(9\) as \({3}^{2}\).
\[\frac{3\sqrt[3]{3}\times 4\sqrt[3]{{3}^{2}}}{{64}^{\frac{2}{3}}\times {27}^{\frac{2}{3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{3\sqrt[3]{3}\times 4\times {3}^{\frac{2}{3}}}{{64}^{\frac{2}{3}}\times {27}^{\frac{2}{3}}}\]
Simplify \(3\sqrt[3]{3}\times 4\times {3}^{\frac{2}{3}}\) to \(12\sqrt[3]{3}\times {3}^{\frac{2}{3}}\).
\[\frac{12\sqrt[3]{3}\times {3}^{\frac{2}{3}}}{{64}^{\frac{2}{3}}\times {27}^{\frac{2}{3}}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{12\times 3}{{64}^{\frac{2}{3}}\times {27}^{\frac{2}{3}}}\]
Simplify \(12\times 3\) to \(36\).
\[\frac{36}{{64}^{\frac{2}{3}}\times {27}^{\frac{2}{3}}}\]
Rewrite \(64\) as \({2}^{6}\).
\[\frac{36}{{({2}^{6})}^{\frac{2}{3}}\times {27}^{\frac{2}{3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{36}{{2}^{\frac{6\times 2}{3}}\times {27}^{\frac{2}{3}}}\]
Simplify \(6\times 2\) to \(12\).
\[\frac{36}{{2}^{\frac{12}{3}}\times {27}^{\frac{2}{3}}}\]
Simplify \(\frac{12}{3}\) to \(4\).
\[\frac{36}{{2}^{4}\times {27}^{\frac{2}{3}}}\]
Simplify \({2}^{4}\) to \(16\).
\[\frac{36}{16\times {27}^{\frac{2}{3}}}\]
Rewrite \(27\) as \({3}^{3}\).
\[\frac{36}{16{({3}^{3})}^{\frac{2}{3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{36}{16\times {3}^{\frac{3\times 2}{3}}}\]
Simplify \(3\times 2\) to \(6\).
\[\frac{36}{16\times {3}^{\frac{6}{3}}}\]
Simplify \(\frac{6}{3}\) to \(2\).
\[\frac{36}{16\times {3}^{2}}\]
Simplify \({3}^{2}\) to \(9\).
\[\frac{36}{16\times 9}\]
Simplify \(16\times 9\) to \(144\).
\[\frac{36}{144}\]
Simplify.
\[\frac{1}{4}\]
Decimal Form: 0.25
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