`a) ( x - 1/2 )^3 = ( 2/5 )^6`
`=> ( x - 1/2 )^3 = ( 4/25)^3`
`=> x - 1/2 = 4/25`
`=> x = 1/2 + 4/25`
`=> x = 29/50`
`b) ( 3/2x - 5)^7 - ( 2/3 )^{14} = 0`
`=> ( 3/2x - 5)^7 = ( 2/3 )^{14}`
`=> ( 3/2x - 5 )^7 = ( 4/9)^7`
`=> 3/2x - 5 = 4/9`
`=> 3/2x = 5 + 4/9 = 49/9`
`=> x = 49/9 : 3/2 = 98/27`
`c) ( 2x - 5/2 )^5 = ( 1/2)^{15}`
`=> ( 2x - 5/2 )^5 = ( 1/8)^5`
`=> 2x - 5/2 = 1/8`
`=> 2x = 5/2 + 1/8 = 21/8`
`=> x = 21/8 : 2 = 21/16`
`d) ( 2x - 5/7 )^{2001} = ( 8/125 )^{667}`
`=> ( 2x - 5/7 )^{3(667)} = ( 8/125 )^{667}`
`=> ( 2x - 5/7)^3 = ( 2/5)^3`
`=> 2x - 5/7 = 2/5`
`=> 2x = 5/7 + 2/5`
`=> 2x = 39/35`
`=> x = 39/35 : 2`
`=> x = 39/70`
