Question

Find the value of: $\frac{4}{216^{\frac{2}{3} } } +\frac{1}{256^{\frac{3}{4} } } +\frac{2}{243^{\frac{1}{5} } }$

Answer 1

Answer:

Step-by-step explanation:

first write the denominator in the terms of powers

4/6^3*2/3 +  1/4^4*3/4 + 2/3^5*1/5

=4/36+1/64+2/3

=take lcm

then the lcm +576

64+9+284/576

357/576=119/192

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Answer 2

Step-by-step explanation:

$\bf \underline{Evaluate-}$

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

$\bf \underline{Solution-}$

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

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

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

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

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

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

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

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

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

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

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