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  • Find the value of .4 by (216) power -2 by 3 + 1 by (256) power -3 by 4 + 2 by (243) power -1 by 5

Find the value of \frac{4}{\left ( 216 \right )^{\frac{-2}{3}}}+\frac{1}{\left ( 256 \right )^{\frac{-3}{4}}}+\frac{2}{\left ( 243 \right )^{\frac{-1}{5}}}.

Answers (1)

Answer. 214
Solution. We have, \frac{4}{\left ( 216 \right )^{\frac{-2}{3}}}+\frac{1}{\left ( 256 \right )^{\frac{-3}{4}}}+\frac{2}{\left ( 243 \right )^{\frac{-1}{5}}}
We know that
216 = 6.6.6 = 63
256 = 4.4.4.4 = 44
243 = 3.3.3.3.3 = 35
So, \frac{4}{\left ( 216 \right )^{\frac{-2}{3}}}+\frac{1}{\left ( 256 \right )^{\frac{-3}{4}}}+\frac{2}{\left ( 243 \right )^{\frac{-1}{5}}}

= \frac{4}{\left ( 6^{3} \right )^{\frac{-2}{3}}}+\frac{1}{\left ( 4^{4} \right )^{\frac{-3}{4}}}+\frac{2}{\left ( 3 ^{5}\right )^{-\frac{1}{5}}}
= \frac{4}{\left ( 6 \right )^{3\times \frac{-2}{3}}}+\frac{1}{\left ( 4 \right )^{4\times \frac{-3}{4}}}+\frac{2}{\left ( 3 \right )^{5\times \frac{-1}{5}}}
\because \left ( \left ( a \right )^{m} \right )^{n}= \left ( a \right )^{mn}
= \frac{4}{6^{-2}}+\frac{1}{4^{-3}}+\frac{2}{3^{-1}}
= 4 × 62 + 43 + 2 × 3    
\because \frac{1}{\left ( a \right )^{-n}}= \left ( a \right )^{n}                                  
= 4 × 36 + 64 + 6
= 144 + 70
= 214

Hence the answer is 214

 

Posted by

infoexpert27

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