Question

Find the value of ${\left(27\right)}^{-\frac{2}{3}}+{\left({\left(2^{-\frac{2}{3}}\right)}^{-\frac{5}{3}}\right)}^{-\frac{9}{10}}$

• A. $\frac{1}{9}$
• B. $\frac{2}{9}$
• C. $\frac{11}{18}$
• D. 1

Answer 1

Answer: (C)

$\frac{11}{18}$

As Given ${\left(27\right)}^{-\frac{2}{3}}+{\left({\left(2^{-\frac{2}{3}}\right)}^{-\frac{5}{3}}\right)}^{-\frac{9}{10}}$
$={\left({\left(3\right)}^3\right)}^{-\frac{2}{3}}+{\left(2^{-\frac{2}{3}}\right)}^{-\frac{5}{3}\cdot -\frac{9}{10}}$
$=3^{-2}+{\left(2^{-\frac{2}{3}}\right)}^{\frac{3}{2}}$
$3^{-2}+2^{-\frac{2}{3}\cdot \frac{3}{2}}$
$=3^{-2}+2^{-1}$
$=\frac{1}{3^2}+\frac{1}{2}$
$=\frac{1}{9}+\frac{1}{2}$
$=\frac{2+9}{18}$
$=\frac{11}{18}$