Simplify; [(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)
- \(\frac{3}{4}\)
- \(\frac{9}{16}\)
-
\(\frac{3}{8}\)
- \(\frac{1}{4}\)
The correct answer is: C
Explanation
[(\(\frac{16}{9}\))\(^{\frac{-3}{2}}\) x 16\(^{\frac{-3}{4}}\)]\(^{\frac{1}{3}}\)
= [(\(\frac{9}{16}\))]\(^{\frac{3}{2}}\) x [(\(\frac{1}{16}\))\(^{\frac{3}{4}}\)]\(^{\frac{1}{3}}\)
= [(\(\sqrt{\frac{9}{16}}\))\(^3\) x (4\(\sqrt{\frac{1}{16}})^3\)]\(^{\frac{1}{3}}\)
= [(\(\frac{3}{4})^3 \times (\frac{1}{2})^3\)]\(^\frac{1}{3}\)
(\(\frac{27}{64} \times \frac{1}{8}\))\(^\frac{1}{3}\) = \({3}\sqrt{\frac{27}{64} \times \frac{1}{8}}\)
= \(\frac{3}{4} \times \frac{1}{2}\) = \(\frac{3}{8}\)