Calculate.
\[\frac{{5}^{3}\times {243}^{\frac{3}{5}}}{{16}^{\frac{5}{4}}\times {8}^{\frac{4}{3}}}\]
Simplify \({5}^{3}\) to \(125\).
\[\frac{125\times {243}^{\frac{3}{5}}}{{16}^{\frac{5}{4}}\times {8}^{\frac{4}{3}}}\]
Rewrite \(243\) as \({3}^{5}\).
\[\frac{125{({3}^{5})}^{\frac{3}{5}}}{{16}^{\frac{5}{4}}\times {8}^{\frac{4}{3}}}\]
Use this rule: \({({x}^{a})}^{b}={x}^{ab}\).
\[\frac{125\times {3}^{\frac{5\times 3}{5}}}{{16}^{\frac{5}{4}}\times {8}^{\frac{4}{3}}}\]
Simplify \(5\times 3\) to \(15\).
\[\frac{125\times {3}^{\frac{15}{5}}}{{16}^{\frac{5}{4}}\times {8}^{\frac{4}{3}}}\]
Simplify \(\frac{15}{5}\) to \(3\).
\[\frac{125\times {3}^{3}}{{16}^{\frac{5}{4}}\times {8}^{\frac{4}{3}}}\]
Simplify \({3}^{3}\) to \(27\).
\[\frac{125\times 27}{{16}^{\frac{5}{4}}\times {8}^{\frac{4}{3}}}\]
Simplify \(125\times 27\) to \(3375\).
\[\frac{3375}{{16}^{\frac{5}{4}}\times {8}^{\frac{4}{3}}}\]
Calculate.
\[\frac{3375}{{2}^{5}\times {8}^{\frac{4}{3}}}\]
Simplify \({2}^{5}\) to \(32\).
\[\frac{3375}{32\times {8}^{\frac{4}{3}}}\]
Calculate.
\[\frac{3375}{32\times {2}^{4}}\]
Simplify \({2}^{4}\) to \(16\).
\[\frac{3375}{32\times 16}\]
Simplify \(32\times 16\) to \(512\).
\[\frac{3375}{512}\]
Decimal Form: 6.591797
3375/512
