14 4 Given that n^(-(4)/(5))=((1)/(2))^4 where ngt 0 find the value of n. (Total for Qu

We begin by converting the right hand expression, ie., \( (\frac{1}{2})^{4} \). This involves raising \( \frac{1}{2} \) to the power \( 4 \). Plugging this into a calculator or calculating manually, it gives:<br />\[(\frac{1}{2})^{4}= (\frac{1}{2})\times(\frac{1}{2})\times(\frac{1}{2})\times(\frac{1}{2})=\frac{1}{16}.\]<br /><br />Then, we equate \( \frac{1}{16} \) to \( n^{-\frac{4}{5}} \). The negative notation of the exponent signifies the reciprocal of the value or base (which is `n` in this case). This means \( \frac{1}{n^{4/5}} = \frac{1}{16} \). Eastings, this means that \( n^{4/5} = 16 \).<br /><br />Finally, to get the value of \( n \), we need to get rid of the \( \frac{4}{5} \) exponent. We do this by raising both sides to the power of \( \frac{5}{4} \), which gives \( n^{(4/5 * 5/4)} = n^1 = n \). This implies<br />\[ n = 16^{\frac{5}{4}} \] <br /><br />Calculating \( 16^{\frac{5}{4}} \), we get the accurate answer: