a; 23.17 + 23.83 - 14
= 23.(17 + 83) - 14
= 8.100 - 14
= 800 - 14
= 786
b; -176 + 197 - (-76 + 97)
= -176 + 197 + 76 - 97
= -(176 - 76) + (197 - 97)
= - 100 + 100
= 0
c; 2022 - [45 - (6 - 1)2 ] + 20210
= 2022 - [45 - 52] + 1
= 2022 + 1 - [45 - 25]
= 2023 - 20
= 2003
a) \(2^3.17+2^3.83-14\)
\(=2^3.\left(17+83\right)-14\)
\(=8.100-14\)
\(=800-14\)
\(=786\)
b) \(-176+197-\left(-76+97\right)\)
\(=-176+197+76-97\)
\(=\left(-176+76\right)+\left(197-97\right)\)
\(=-100+100\)
\(=0\)
c) \(2022-\left[45-\left(6-1\right)^2\right]+2021^0\)
\(=2022-\left[45-5^2\right]+1\)
\(=2022-\left[45-25\right]+1\)
\(=2022-20+1\)
\(=2002+1=2003\)