Part 1
[tex]6- \frac{18-3^2}{4+(2-3)} =6- \frac{18-9}{4+(-1)} \\ \\ =6- \frac{9}{4-1} =6- \frac{9}{3} =6-3 \\ \\ =3[/tex]
Part 2
[tex]7-8\div4(3^2-1)=7-8\div4(9-1) \\ \\ =7-8\div4(8)=7-8\div32=7- \frac{1}{2} \\ \\ =6 \frac{1}{2} = \frac{13}{2} [/tex]
Part 3
[tex]2-2(2-5)^2+3^2=2-2(-3)^2+9 \\ \\ =2-2(9)+9=2-18+9=-7[/tex]
Part 4
[tex](5^2-9\cdot3)^2-11=(25-27)^2-11 \\ \\ =(-2)^2-11=4-11=-7[/tex]
Part 5
[tex][(2-3)^2-5]\cdot4=[(-1)^2-5]\cdot4 \\ \\ =(1-5)\cdot4=-4\cdot4=-16[/tex]
Part 6
[tex]12-11\cdot2+16\div8=12-22+2 \\ \\ =-8[/tex]
Part 7
[tex]-5+1\cdot3-(7-2^3)=-5+3-(7-8) \\ \\ =-2-(-1)=-2+1=-1[/tex]
Part 8
[tex]8+2\cdot3-14\div7=8+6-2 \\ \\ =12[/tex]
Part 9
[tex](8-2)^2+\frac{1}{4}[4-3(6-10)]=6^2+\frac{1}{4}[4-3(-4)] \\ \\ =36+\frac{1}{4}[4-(-12)]=36+\frac{1}{4}(4+12)=36+\frac{1}{4}(16) \\ \\ =36+4=40[/tex]
Part 10
[tex]7+(2-3^2)\cdot5=7+(2-9)\cdot5 \\ \\ =7+(-7)\cdot5=7+(-35)=7-35 \\ \\ =-28[/tex]
Part 11
[tex]3-2[2^3+(-1)^3]=3-2[8+(-1)] \\ \\ =3-2(8-1)=3-2(7)=3-14 \\ \\ -11[/tex]
Part 12
[tex]18+6\div3(2^2+5)=18+6\div3(4+5) \\ \\ =18+6\div3(9)=18+6\div27=18+ \frac{2}{9} \\ \\ =18 \frac{2}{9}[/tex]
