`1)`
`a) (2/3)^3 - (3/4)^2. (-1)^5`
`= 2^3/3^3 - 3^2/4^2. (-1)`
`= 8/27 - 9/16. (-1)`
`= 8/27 + 9/16`
`= 128/432 + 243/432`
`= 371/432`
`b) sqrt{(-7)^2} + sqrt{25/16} - 3/2`
`= sqrt{49} + sqrt{5^2/4^2} - 3/2`
`= sqrt{7. 7} + sqrt{5/4. 5/4} - 3/2`
`= 7 + 5/4 - 3/2`
`= 28/4 + 5/4 - 6/4`
`= 27/4`
`c) (5^4. 20^4)/(25^5. 4^5)`
`= (5^4. (5. 4)^4)/((5^2)^5. 4^5)`
`= (5^4. 5^4. 4^4)/(5^10. 4^5)`
`= (5^8. 4^4)/(5^8. 5^2. 4^4. 4)`
`= (5^8. 4^4)/((5^2. 4)(5^8. 4^4))`
`= 1/(5^2. 4)`
`= 1/(25. 4)`
`= 1/100`
`d) (2^12. 3^5 - 4^6. 3^6)/(2^12. 9^3 + 8^4. 3^5)`
`= (2^12. 3^5 - (2^2)^6. 3^6)/(2^12. (3^2)^3 + (2^3)^4 + 3^5)`
`= (2^12. 3^5 - 2^12. 3^6)/(2^12. 3^6 + 2^12. 3^5)`
`= (2^12. 3^5. (1 - 3))/(2^12. 3^5. (3 + 1))`
`= (1 - 3)/(3 + 1)`
`= (-2)/4`
`= -1/2`