`a) 5^18:5^16+1^2020+2020^0`
`=5^(18-16)+1+1`
`=5^2+1+1`
`=25+2`
`=27`
`b)580:[180-2(5^3-4^3)]+7^3`
`=580:[180-2.61]+343`
`=580:[180-122]+343`
`=580:58+343`
`=10+343`
`=353`
`c)12.4^3-2^2 . 5^2+12. 6^2`
`=12.64-4.25+12.36`
`=768-100+432`
`=668+432`
`=1100`
`d){106-[64+4(17-14)^2]}^3`
`={106-[64+4.9]}^3`
`={106-100}^3`
`=6^3`
`=216`
`e)15^2021:15^2020+2021^0`
`=15^(2021-2020)+1`
`=15+1`
`=16`