Simplify
(i) $\left(\frac{81}{49}\right)^{-\frac{3}{2}}$
(ii) $(14641)^{0.25}$
(iii) $\left(\frac{32}{243}\right)^{-\frac{4}{5}}$
(iv) $\left(\frac{7776}{243}\right)^{-\frac{3}{5}}$
(i) $\left(\frac{81}{49}\right)^{-\frac{3}{2}}$
$\left(\frac{81}{49}\right)^{-\frac{3}{2}}=\left[\left(\frac{9}{7}\right)^{2}\right]^{-\frac{3}{2}}$
$=\left(\frac{9}{7}\right)^{-3}$
$=\left(\frac{7}{9}\right)^{3}$
$=\frac{343}{729}$
(ii) $(14641)^{0.25}$
$(14641)^{0.25}=(14641)^{\frac{25}{100}}$
$=(14641)^{\frac{1}{4}}$
$=\left[(11)^{4}\right]^{\frac{1}{4}}$
$=11$
(iii) $\left(\frac{32}{243}\right)^{-\frac{4}{5}}$
$\left(\frac{32}{243}\right)^{-\frac{4}{5}}=\left(\frac{243}{32}\right)^{\frac{4}{5}}$
$=\left[\left(\frac{3}{2}\right)^{5}\right]^{\frac{4}{5}}$
$=\left(\frac{3}{2}\right)^{4}$
$=\frac{81}{16}$
(iv) $\left(\frac{7776}{243}\right)^{-\frac{3}{5}}$
$\left(\frac{7776}{243}\right)^{-\frac{3}{5}}=\left(\frac{243}{7776}\right)^{\frac{3}{5}}$
$=\left[\left(\frac{3}{6}\right)^{5}\right]^{\frac{3}{5}}$
$=\left(\frac{1}{2}\right)^{3}$
$=\frac{1}{8}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.