Question

simplify 4 upon 216 ki power minus 2 upon 3 + 1 upon 256 ki power minus 3 upon 4 + 2 upon 243 ki power minus 1 upon 5 please solve

Answer 1

question

(4/216)^-2/3+ (1/256)^-3/4+(2/243)^-1/5

= (54)⅔ + (256)¾ + (243/2)¹/5

[ 54=3³×2;. 256= 4⁴ , 243= 3^5 ] therefore

= 9(2)⅔+ 4³+ 3(1/2)¹/5

= 64+ 9×2⅔+3×1/2¹/5

this is simplest form

Answer 2

$\bf \underline{Evaluate-}$

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

$\bf \underline{Solution-}$

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

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

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

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

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

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

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

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

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

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

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