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Đáp án + Giải thích các bước giải:

`a)`

`( 1/2 )^5 : ( 1/4 )^2 `

`= ( 1/2 )^5 : [ ( 1/2 )^2 ]^2`

`= ( 1/2 )^5 : ( 1/2 )^4`

`= ( 1/2 )^( 5 -4 ) `

`= ( 1/2 )^1 `

`= 1/2`

`b)`

`( 5/2 )^3. ( 4/5 )^3`

`= ( 5/2. 4/5 )^3`

`= 2^3`

`= 8 `

`c)`

`( -1/2 )^2. ( 2/5 )^2`

`= ( 1/2 )^2. ( 2/5 )^2`

`= ( 1/2. 2/5 )^2`

`= ( 1/5 )^2`

`= 1/25`

`d)`

`( 1/9 )^2. ( 1/3 )^3`

`= [ ( 1/3 )^2 ]^2 : ( 1/3 )^3`

`= ( 1/3 )^4 : ( 1/3 )^3`

`= ( 1/3 )^( 4 - 3 ) `

`= ( 1/3 )^1`

`= 1/3`

`e)`

`( 5/4 )^2 : ( -35/24 )^2 `

`= ( 5/4 )^2 : ( 35/24 )^2 `

`= ( 5/4 : 35/24 )^2`

`= ( 5/4. 24/35 )^2`

`= ( (5. 4. 6 )/( 4. 5. 7 ) )^2`

`= ( 6/7 )^2`

`= 36/49`

`f)`

`( 9/10 )^5 : ( -27/20 )^5 `

`= [ 9/10 : ( -27/20 ) ]^5`

`= [ 9/10. ( -20/27 ) ]^5 `

`= [ ( 9. 10. ( -2 ) )/( 10. 9. 3 ) ]^5`

`= ( -2/3 )^5`

`= (-32)/243`