Question

1. Simplify(216)2/3+(256)3/4+(243)1/5

Answer 1

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

= ((6^3)^(2/3)) + ((4^4)^(3/4)) + ((3^5)^(1/5))

= 6^2 + 4^3 + 3

= 36 + 64 + 3

= 103.

Please mark it as the brainliest answer for the question.

Answer 2

Step-by-step explanation:

$\bf \underline{Evaluate-}$

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

$\bf \underline{Solution-}$

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

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

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

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

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

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

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

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

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

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

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