Question

$\frac{1}{{\left(216\right)}^{\frac{-2}{3}}}+\frac{1}{{\left(256\right)}^{\frac{-3}{4}}}+\frac{1}{{\left(243\right)}^{\frac{-1}{5}}}$ is equal to:

• A. $103$
• B. $105$
• C. $107$
• D. $101$

Answer 1

Answer: (A)

$103$

Given expression

$=\frac{1}{{\left(216\right)}^{\frac{-2}{3}}}+\frac{1}{{\left(256\right)}^{\frac{-3}{4}}}+\frac{1}{{\left(243\right)}^{\frac{-1}{5}}}$

$=\frac{1}{(6^3{)}^{\frac{-2}{3}}}+\frac{1}{(4^4{)}^{\frac{-3}{4}}}+\frac{1}{(3^5{)}^{\frac{-1}{5}}}$

$=\frac{1}{6^{-2}}+\frac{1}{4^{-3}}+\frac{1}{3^{-1}}$

$=6^2+4^3+3$

$=36+64+3$

$=103$