Question:
Evaluate $\left(\frac{81}{49}\right)^{\frac{-3}{2}}$
Solution:
$\left(\frac{81}{49}\right)^{\frac{-3}{2}}=\left(\frac{49}{81}\right)^{\frac{3}{2}}$
$=\left(\frac{7^{2}}{9^{2}}\right)^{\frac{3}{2}}$
$=\left[\left(\frac{7}{9}\right)^{2}\right]^{\frac{3}{2}}$
$=\left(\frac{7}{9}\right)^{3}$
$=\frac{7^{3}}{9^{3}}$
$=\frac{343}{729}$
Hence, $\left(\frac{81}{49}\right)^{\frac{-3}{2}}=\frac{343}{729}$.
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