Question

Hii guys help me please

Answer 1

1 . { (1/2)^(-3)  -  (1/3)^(-2)  } ÷ (1/5)^(-2)

Sol : Using identity ( a / b )^(-n ) = ( b / a )^n.

= { ( 2 )³ - ( 3 )² } ÷ (5)²

= { 8 - 9 } ÷ 25

= 1 ÷ 25

= 1 / 25.


2. { (2/3)^(-2)  -  (3/4)^(-1) }^(-2)

Sol : Using identity ( a / b )^(-n ) = ( b / a )^n.

= { ( 3 / 2)² - (4 / 3 ) }^( -2 )

= { ( 9 / 4 ) - ( 4 / 3) } ^ ( - 2 )

            27 - 16
= {  ----------------------- } ^ ( - 2 )
               12

= ( 11 / 12 ) ^ ( - 2 )

 Using identity ( a / b )^(-n ) = ( b / a )^n.


= ( 12 / 11 )² 

= 144 / 121.


3. { ( 1 / 2 )^ ( -3 )  ÷ ( 1 / 3 )^ ( -2 ) } ^ ( -1 )  ÷ ( 1 / 4 )^ ( -1 )

Sol : Using identity ( a / b )^(-n ) = ( b / a )^n.

= { ( 2 )³  ÷ ( 3 )² } ^ ( - 1 )  ÷ ( 4 )^1

= { 8 ÷ 9 } ^ ( - 1 ) ÷ 4

 Using identity ( a / b )^(-n ) = ( b / a )^n.

= ( 9 / 8 ) ÷ 4

=  ( 9 / 8 ) x ( 1 / 4 )

= 9 / 32.

 
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