Question

Simplify :-
$\red{\bf \dfrac{3}{216^{\frac{-2}{3}}} + \dfrac{2}{256^{\frac{-3}{4}}} + \dfrac{2}{243^{\frac{-1}{5}}} }$

No spam​

Answer 1

♣ Qᴜᴇꜱᴛɪᴏɴ :

$\sf{\dfrac{3}{216^{\tfrac{-2}{3}}}+\dfrac{2}{256^{\tfrac{-3}{4}}}+\dfrac{2}{243^{\tfrac{-1}{5}}}}$

★═════════════════★

♣ ᴀɴꜱᴡᴇʀ :

242

★═════════════════★

♣ ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴꜱ :

$\dfrac{3}{216^{\tfrac{-2}{3}}}+\dfrac{2}{256^{\tfrac{-3}{4}}}+\dfrac{2}{243^{\tfrac{-1}{5}}}$

$\sf{=\dfrac{3}{\left(6^3\right)^{\tfrac{-2}{3}}}+\dfrac{2}{\left(4^4\right)^{\tfrac{3}{4}}}}+\dfrac{2}{\left(3^5\right)^{\tfrac{-1}{5}}}}$

$\sf{=\dfrac{3}{\left(6\right)^{\tfrac{-6}{3}}}+\dfrac{2}{\left(4\right)^{\tfrac{4}{4}}}}+\dfrac{2}{\left(3\right)^{\tfrac{-5}{5}}}}$

$\sf{=\dfrac{3}{(6)^{-2}}+\dfrac{2}{(4)^{-3}}+\dfrac{2}{(3)^{-1}}}$

$\sf{=3 \times 6^{2}+2 \times 4^{3}+2 \times 3^{1}}$

$\begin{array}{l}\sf{=108+128+6} \\\\\\\sf{=242}\end{array}$

Answer 2

$\huge \rm \red{\underline{\underline{Answer :- }}}$

The answer is 242 ;)