Question

Simplify it
and please help me fast.

Answer 1

Q. Simplification »

[ ( 3 / 2 )⁻² ]²

= [ ( 2 / 3 )² ]²

= ( 2 / 3 )²*²

= ( 2 / 3 )⁴

= ( 2 )⁴ / ( 3 )⁴

= 16 / 81

Answer » ( 16 / 81 )

Reasons »

❖ We know,

(a / b)⁻¹ = (b / a)¹

Hence, (3 / 2)⁻² = (2 / 3)²

❖ We know,

[ (a / b)² ]² = (a / b)²*² = (a / b)⁴

Hence, [ (2 / 3)² ]² = (2 / 3)²*² = (2 / 3)⁴

❖ We know,

(a / b)² = ( a )² / ( b )²

Hence, ( 2 / 3 )⁴ = ( 2 )⁴ / ( 3 )⁴ = 16 / 81

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