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  • Simplify : (256) power -(4 power -3by 2)

Simplify : \left ( 256 \right )^{-\left ( 4^{\frac{-3}{2}} \right )}

Answers (1)

Answer. 248
Solution.  Given, \left ( 256 \right )^{-\left ( 4^{\frac{-3}{2}} \right )}
We know that,
256 = 2.2.2.2.2.2.2.2 = 28

\left ( 256 \right )^{-\left ( 4^{\frac{-3}{2}} \right )}  = \left ( 2^{8} \right )^{\left ( -4 \right )\times \left ( -\frac{3}{2} \right )}                                   

\because \left ( \left ( a \right ) ^{m}\right )^{n}= \left ( a \right )^{mn}

=\left ( 2 \right )^{8\times \left ( -4 \right )\times \left ( -\frac{3}{2} \right )}
= 2^{8\times 4\times \frac{3}{2}}= 2^{8\times 2\times 3}= 2^{48}
Hence the answer is 248

Posted by

infoexpert27

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