Question

$\text{Find the value of}\frac{1}{(216{)}^{-\frac{2}{3}}}+\frac{1}{(256{)}^{-\frac{3}{4}}}+\frac{2}{(243{)}^{-\frac{1}{5}}}$

• A.
  100
• B.
  105
• C.
  106
• D.
  110

Answer 1

The correct option is C

106
$\frac{1}{(216{)}^{-2/3}}+\frac{1}{(256{)}^{-3/4}}+\frac{2}{(243{)}^{-1/5}}=\frac{1}{(6^3{)}^{-2/3}}+\frac{1}{(4^4{)}^{-3/4}}+\frac{2}{(3^5{)}^{-1/5}}\left(\right(a^m{)}^n=a^{m\times n})=\frac{1}{(6{)}^{3\times -\frac{2}{3}}}+\frac{1}{(4{)}^{4\times -\frac{3}{4}}}+\frac{2}{(3{)}^{5\times --\frac{1}{5}}}=\frac{1}{6^{-2}}+\frac{1}{4^{-3}}+\frac{2}{3^{-1}}(a^{-m}=\frac{1}{a^m})=6^2+4^3+2\times 3=36+64+6=106$