Question

$(2^5 \div 2^8) ^5 \times 2^ - 5$
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Answer 1

★Answer★

${ \tt{ \implies {( \dfrac{ {2}^{5} }{ {2}^{8} } ) }^{5} \times {2}^{ - 5} }}$

${ \rm{using \: (\dfrac{a}{b} )^{n} = \dfrac{ {a}^{n} }{ {b}^{n} } }} \\ \\ { \rm{ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {x}^{ - y} = \frac{1}{ {x}^{y} } }}$

${ \tt{ \implies \dfrac{ \cancel{2}^{25} }{ \cancel{2}^{40} } \times \dfrac{1}{ \cancel{2}^{5} } = \dfrac{1}{ {2}^{8} } = {2}^{ - 8} }}$

Answer 2

${ (\dfrac{ {2}^{5} }{ {2}^{8} } )}^{5} \times {2}^{ - 5} ={2}^{-8}$