Bài `9:`

`a)` `(3^6 . 45^4 - 15^13 . 1/(5^9))/(27^4 . 25^3 + 45^6) `

`=(3^6 . 45^4 - 15^13 . 5^(-9))/(27^4 . 25^3 + 45^6) `

`= (3^6 . (3^2 . 5)^4 - (3 . 5)^13 . 5^(-9))/((3^3)^4 . (5^2)^3 + (3^2 . 5)^6)`

`= (3^6 . 3^8 . 5^4-3^13 . 5^13 . 5^(-9))/(3^12 . 5^6 + 3^12 . 5^6)`

`= (3^14 . 5^4-3^13 . 5^4)/(3^12 . 5^6+3^12 . 5^6)`

`=(3^13 . 5^4 . (3-1))/(2 . 3^12 . 5^6)`

`= (3 . 2)/(2 . 5^2)`  

`=3/25`

`b)` `\frac{(\frac{2}{5})^{7}.5^{7}+(\frac{9}{4})^{3}:(\frac{3}{16})^{3}}{2^{7}.5^{2}+512}`

`=\frac{(\frac{2}{5}.5)^{7}+\frac{9^{3}}{4^{3}}:\frac{3^{3}}{16^{3}}}{2^{7}.5^{2}+2^{7}.2^{2}}`

`=\frac{2^{7}+\frac{(3^{2})^{3}}{4^{3}}.\frac{(4^{2})^{3}}{3^{3}}}{2^{7}.(5^{2}+2^{2})}`

`=\frac{2^{7}+\frac{3^{6}.4^{6}}{4^{3}.3^{3}}}{2^{7}.(25+4)}`

`=\frac{2^{7}+\frac{(3.4)^{6}}{(4.3)^{3}}}{2^{7}.29}`

`=\frac{2^{7}+(3.4)^{3}}{2^{7}.29}`

`=\frac{2^6 . 2^1 +3^{3}.2^{6}}{2^{7}.29}`

`=\frac{2^{6}.(2+3^{3})}{2^{7}.29}`

`=\frac{2^6 . (2 + 27)}{2.29}`

`=\frac{2+27}{2.29}`

`=\frac{29}{2.29}`

`=1/2`

Bài `10:`

`a)` `( (2/3)^3 . (-3/4)^2 . (-1)^5)/( (2/5)^2 . (-5/12)^2)`

` = ( (2/3 . (-3)/4)^2 . (2/3) . (-1))/( (2/5 . (-5)/12)^2)`

` = ( (-1/2)^2 . (-2)/3)/( (-1/6)^2)`

` = (1/4 . (-2)/3)/(1/36)`

` = ( -1/6)/(1/36)`

`=-1/6 : 1/36`

`=-1/6 . 36`

`=-6`

`b)` `(4^10 + 8^4)/(4^5+8^6)`

`=((2^2)^10 + (2^3)^4)/((2^2)^5 + (2^3)^6)`

`=(2^20 + 2^12)/(2^10 + 2^18)`

`=(2^12 . (2^8 + 1))/(2^10 . (2^8+1))`

`=(2^2 . 2^10)/(2^10)`

`=2^2`

`=4`