Question

(9/16)^(3/2)

Answer 1

27/64

Answer 2

\[\large \left(\frac{9}{16}\right)^{\frac{3}{2}}\]


\[\large \left(\sqrt{\frac{9}{16}}\right)^{3}\]


\[\large \left(\frac{\sqrt{9}}{\sqrt{16}}\right)^{3}\]


\[\large \left(\frac{3}{4}\right)^{3}\]


\[\large \frac{3^3}{4^3}\]


\[\large \frac{27}{64}\]
So \[\large \left(\frac{9}{16}\right)^{\frac{3}{2}}=\frac{27}{64}\]

Answer 3

Another way to look at it is:
\[(9/16)^{3/2}=(9/16)^{2/2}(9/16)^{1/2}=9/16(\sqrt{9/16}=(9/16)(3/4)=27/64\]