Simplify it
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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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