Question
Simplify:
$\Big(\frac{81}{49}\Big)^{-\frac{3}{2}}$
$\Big(\frac{81}{49}\Big)^{-\frac{3}{2}}$
✓
Answer
$\Big(\frac{81}{49}\Big)^{-\frac{3}{2}}$
$=\Big(\frac{49}{81}\Big)^{\frac{3}{2}}$
$=\Big(\frac{7^2}{9^2}\Big)^{\frac{3}{2}}$
$=\frac{7^{2\times\frac{3}{2}}}{9^{2\times\frac{3}{2}}}$
$=\frac{7^3}{9^3}$
$=\frac{343}{729}$
$=\Big(\frac{49}{81}\Big)^{\frac{3}{2}}$
$=\Big(\frac{7^2}{9^2}\Big)^{\frac{3}{2}}$
$=\frac{7^{2\times\frac{3}{2}}}{9^{2\times\frac{3}{2}}}$
$=\frac{7^3}{9^3}$
$=\frac{343}{729}$
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