Question

${\left(\frac{81}{16}\right)}^{-3/4}=?$
(a) $\frac{4}{9}$
(b) $\frac{9}{4}$
(c) $\frac{27}{8}$
(d) $\frac{8}{27}$

Answer 1

(d) $\frac{8}{27}$

$$\begin{gathered} \because {\left(\frac{81}{16}\right)}^{-\frac{3}{4}} \\ \therefore {\left(\frac{16}{81}\right)}^{\frac{3}{4}} \\ ={\left\{{\left(\frac{16}{81}\right)}^{\frac{1}{4}}\right\}}^3 \\ ={\left[{\left\{{\left(\frac{2}{3}\right)}^4\right\}}^{\frac{1}{4}}\right]}^3 \\ ={\left(\frac{2}{3}\right)}^3 \\ =\frac{8}{27} \end{gathered}$$