1.
a)
`2^3 + 3^2 - 4^2`
`= 8 + 9 - 16`
`= 17 - 16`
`= 1`
b)
`3^2 . 5 - 2^2 . 3 + 3^3`
`9 . 5 - 4 . 3 + 27`
`= 45 - 12 + 27`
`= 33 + 27`
`= 60`
c)
`5^2 . 2 - 2^3 . 3 + 5 . 4^2`
`= 25 . 2 - 8 . 3 + 5 . 16`
`= 50 - 24 + 80`
`= 26 + 80`
`= 106`
d)
`5^10 : 5^8 - 3^6 : 3^4 + 15`
`= 5^2 - 3^2 + 15`
`= 25 - 9 + 15`
`= 16 + 15`
`= 31`
e)
`20 - (2^2 - 3)^0`
`= 20 - 1`
`= 19`
2.
a)
`(x+3^2) - 5 . 2^2 = 3^3`
`(x+9) - 5 . 4 = 27`
`(x+9) -20 = 27`
`(x+9) = 27 + 20`
`(x+9) = 47`
`x = 47 - 9`
`x = 38`
b)
`3^3 - 2(x - 4^2) = 5`
`27 - 2(x-16) = 5`
`2(x-16) = 27 - 5`
`2(x-16) = 22`
`x-16 = 22/2`
`x-16 = 11`
`x = 11 + 16`
`x = 27`
c)
`7^2 - 2(x - 5^2) = 3^3`
`49 - 2(x - 25) = 27`
`2(x - 25) = 49 - 27`
` 2(x - 25) = 22`
`x - 25 = 22/2`
`x - 25 = 11`
`x = 11 + 25`
`x = 36`
d)
`(x+1)^3 = 27`
`(x+1)^3 = 3^3`
`x+1 = 3`
`x = 3-1`
`x = 2`
e)
`(x-2)^2 = 64`
`(x-2)^2 = 8^2`
`x - 2 = 8`
`x = 8+2`
`x = 10`
f)
`(x+4)^2 = 81`
`(x+4)^2 = 9^2`
`x+4 = 9`
`x = 9 - 4`
`x = 5`
g)
`2^x = 8`
`2^x = 2^3`
`x = 3`
