[tex] \text{Given : Which expression is equivalent to} \: \frak{( {8}^{2})^{ - 4}} \\ \\ \odot \quad\frak{ \frac{1}{ {8}^{2}}} \\ \\ \odot \quad\frak{ \frac{ - 1}{8 \cdot8 \cdot8 \cdot8\cdot8\cdot8\cdot8\cdot8}} \\ \\ \odot\quad\frak{ \frac{1}{8 \cdot8 \cdot8 \cdot8\cdot8\cdot8\cdot8\cdot8}} \\ \\ \odot \quad \frak{ {8}^{2} }[/tex]
[tex] \text{Solution : For getting the answer we need to first simplify it } \\ \quad \dashrightarrow \frak{ ({8}^{2}) ^{ - 4} } \\ \\ \quad \dashrightarrow \frak{{8}^{2( - 4)} } \\ \\ \quad \dashrightarrow \frak{ {8}^{( - 8)} } \\ \rm{now \: as \: the \: exponent \: is \: in \: negative \: so \: we \: need \: to \: bring \: 8 \: down \: in \:} \\ \rm{ form \: of \: denominator} \\ \\ \rm{so \: we \: get \: as} : \\ \\ \quad\hookrightarrow \frak{ \frac{1}{ {8}^{8}}} \\ \rm{as \: the \: exponent \: is \: 8 \: so \: we \: get \: to \: know \: that \: 8 \: is \: multplied \: 8 \: times \: with \: 8.} \\ \quad\hookrightarrow\frak{ \frac{1}{8 \cdot8 \cdot8 \cdot8\cdot8\cdot8\cdot8\cdot8}} \\ \\ \therefore \underline{ \boxed{ \sf{ \blue{option \: c} \: i.e.} \: \blue{\frak{\frac{1}{8 \cdot8 \cdot8 \cdot8\cdot8\cdot8\cdot8\cdot8}}} \: is \: the \: \blue{correct \: answer}}}[/tex]
