Question

sum of 4/(216)^-2/3;1/(256)^-3/4;2/(243)^-1/5​

Answer 1

Step-by-step explanation:

$\frac{4}{ {216}^{ - \frac{2}{3} } } + \frac{1}{ {256}^{ - \frac{3}{4} } } + \frac{2}{ {243}^{ - \frac{1}{5} } } \\ = \frac{ {2}^{2} }{ {( {6)}^{3} )}^{ - \frac{2}{3} } } + \frac{1}{ ({( {2)}^{8} )}^{ - \frac{3}{4} } } + \frac{2}{ ({( {3)}^{5} )}^{ - \frac{1}{5} } } \\ = \frac{ {2}^{2} }{ {6}^{ - 2} } + \frac{1}{ {2}^{ - 6} } + \frac{2}{ {3}^{ - 1} } \\ =( {2}^{2} \times {6}^{2}) + ( 1 \times {2}^{6} ) + (2 \times 3) \\ = (4 \times 36) + 64 + 6 \\ = 144 + 64 + 6 \\ = 214$

hope you get your answer

Answer 2

Step-by-step explanation:

$\bf \underline{Evaluate-}$

$\sf\: \dfrac{4}{ ({216)^{ \frac{ - 2}{3} } } } + \dfrac{1}{ ({256)^{ \frac{ - 3}{4} } } } + \dfrac{2}{ ({243)^{ \frac{ - 1}{5} } } }$

$\bf \underline{Solution-}$

$\sf \: \: \implies \: \: \dfrac{4}{ ({216)^{ \frac{ - 2}{3} } } } + \dfrac{1}{ ({256)^{ \frac{ - 3}{4} } } } + \dfrac{2}{ ({243)^{ \frac{ - 1}{5} } } }$

$\sf \: \: \implies \: \: \dfrac{4}{ ({6 \times 6 \times 6)^{ \frac{ - 2}{3} } } } + \dfrac{1}{ ({4 \times 4 \times 4 \times 4)^{ \frac{ - 3}{4} } } } + \dfrac{2}{ ({3 \times 3 \times 3 \times 3 \times 3)^{ \frac{ - 1}{5} } } }$

$\sf \: \: \implies \: \: \dfrac{4}{ ({ {6}^{3} )^{ \frac{ - 2}{3} } } } + \dfrac{1}{ ({ {4}^{4} )^{ \frac{ - 3}{4} } } } + \dfrac{2}{ ({ {3}^{5} )^{ \frac{ - 1}{5} } } }$

$\sf \: \: \implies \: \: \dfrac{4}{ ({ {6} )^{3 \times \frac{ - 2}{3} } } } + \dfrac{1}{ ({ {4} )^{ 4 \times \frac{ - 3}{4} } } } + \dfrac{2}{ ({ {3})^{5 \times \frac{ - 1}{5} } } }$

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

$\sf \: \: \implies \: \: \dfrac{4}{ { \dfrac{1}{ {6}^{2} } } } + \dfrac{1}{ { \dfrac{1}{ {4}^{3} } } } + \dfrac{2}{ { \dfrac{1}{3} } }$

$\sf \: \: \implies \: \: \dfrac{4}{ { \dfrac{1}{ 36} } } + \dfrac{1}{ { \dfrac{1}{ 64 } } } + \dfrac{2}{ { \dfrac{1}{3} } }$

$\sf \: \: \implies \: \: 4 \times 36 + 64 + 2 \times 3$

$\sf \: \: \implies \: \: 144 + 64 + 6$

$\sf \: \: \implies \: \: 144 + 70$

$\bf \: \: \implies \: \: 214$