Question

please give correct answer of this question​

Answer 1

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.

Answer 2

$= \frac{4 {}^{ \frac{ - 1}{2} } \times 2 \frac{1}{2} \times 2 }{ 8 \times 8 {}^{ \frac{ - 1}{2} } }$

$= \frac{( {4)}^{2} \times 4 }{8 \times ( {8)}^{2} }$

$= \frac{16 \times 4}{8 \times 64}$

$= \frac{1}{8}$