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Answer:
Step-by-step explanation:
Given that,
[ 4^-1/2 × 2^1/2 × 2 ] / [ 8 × 8^-1/2 ] (∵" ^ " this symbol means " to the power of " )
= [ (2²)^-1/2 × 2^1/2 × 2] / [( 2³) × ( 2³ )^-1/2 ]
= [ 2^-1 × 2^1/2 × 2 ] / [ 2³ × 2^-3/2 ]
= [ 2^( - 1 + 1/2 + 1 ) ] / [ 2^(3 - 3/2 )] (∵Bases are equal,then powers should be add )
= [ 2^1/2 ] / [ 2^( 6 - 3 / 2 ) ]
= ( 2^1/2 ) / ( 2^3/2 )
= 2^1/2 × 2^( -3/2 )
= 2^( 1/2 -3/2 ) (∵ Bases are equal, then powers should be add )
= 2^( 1- 3 / 2 )
= 2^( - 1/2 ) is the answer.
[tex] = \frac{4 {}^{ \frac{ - 1}{2} } \times 2 \frac{1}{2} \times 2 }{ 8 \times 8 {}^{ \frac{ - 1}{2} } } [/tex]
[tex] = \frac{( {4)}^{2} \times 4 }{8 \times ( {8)}^{2} } [/tex]
[tex] = \frac{16 \times 4}{8 \times 64} [/tex]
[tex] = \frac{1}{8} [/tex]