Question
Simplify:$\Big(\frac{7776}{243}\Big)^{-\frac{3}{5}}$
✓
Answer
$\Big(\frac{7776}{243}\Big)^{-\frac{3}{5}}$$=\Big(\frac{243}{7776}\Big)^{\frac{3}{5}}$
$=\Big(\frac{3^5}{6^5}\Big)^{\frac{3}{5}}$
$=\frac{3^{5\times\frac{3}{5}}}{6^{5\times\frac{3}{5}}}$
$=\frac{3^3}{6^3}$
$=\frac{3\times3\times3}{6\times6\times6}$
$=\frac{1}{8}$
$=\Big(\frac{3^5}{6^5}\Big)^{\frac{3}{5}}$
$=\frac{3^{5\times\frac{3}{5}}}{6^{5\times\frac{3}{5}}}$
$=\frac{3^3}{6^3}$
$=\frac{3\times3\times3}{6\times6\times6}$
$=\frac{1}{8}$
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