Espressioni

215)

$\small 14+2^4+4^2-7-3^2+5^2-7^6÷7^4 =$ $\;\small^{(1)}$

$\small = 14+16+16-7-9+25-7^{6-4} =$

$\small = 46-16+25-7^2 =$

$\small = 30+25-49 =$

$\small = 55-49 = 6$

$\small\text{note: } $

$\small (1) -\text{Nella divisione con basi uguali si sottraggono gli esponenti mantenendo la stessa base.}$

14 + 2^4 + 4^2 - 7 - 3^2 + 5^2 - 7^6 : 7^4;

risolviamo le potenze; la divisione tra potenze di uguale base si risolve sottraendo gli esponenti;

14 + 16 + 16 - 7 - 9 + 25 - 7^2 =

= 14 + 16 + 16 - 7 - 9 + 25 - 49 = 6.

Le addizioni e sottrazioni si svolgono insieme, per non sbagliare le ho raggruppate per controllare  il calcolo.

(14 + 16 + 16) - 7 - 9 + 25 - 49 =

= (46 - 7 - 9) + 25 - 49 =

= (30 + 25) - 49 = 

= 55 - 49 =

= 6.

Ciao @ozuna

216)

$\small 9+5^3-3^2×2^2-(4^5÷4^4)^3+26^2÷2^2-2×10^2 =$

$\small = 9+125-9×4-(4^{5-4})^3+\left(\dfrac{26}{2}\right)^2-2×100 =$

$\small = 134-36-(4^1)^3+13^2-200 =$

$\small = 98-4^{1×3}+169-200 =$

$\small = 98-64+169-200 =$

$\small = (98+169)+(-64-200) =$

$\small = 267+(-264) =$

$\small = 267-264 = 3 $

217)

$\small 6^3×6^0+5×8-2^4×2^2+5^2-3^4-10^2=$

$\small = 6^3×1+40-2^{4+2}+25-81-100 =$

$\small = 6^3+40-2^6+25-81-100 =$

$\small = 216+40-64+25-81-100 =$

$\small = 216+40+25+(-64-81-100) =$

$\small = 281+(-245) =$

$\small = 281-245 = 36$

218)

$\small 8×3×4^2-4^4÷4^2+3^2×5-8^6÷8^4-14^2-6^2×2^2 =$

$\small = 24×16-4^{4-2}+9×5-8^{6-4}-196-36×4 =$

$\small = 384-4^2+45-8^2-196-144 =$

$\small = 384-16+45-64-196-144 =$

$\small = 384+45+(-16-64-196-144) =$

$\small = 429+(-420) =$

$\small = 429-420 = 9$

219)

$\small 9^2-3^4+2^3×2^4-5^2+3^2×5^2-11^2-4×2×5^2 =$

$\small = 81-81+2^{3+4}-25+9×25-121-8×25 =$

$\small = 0+2^7-25+225-121-200 =$

$\small = 128-25+225-121-200 =$

$\small = (128+225)+(-25-121-200) =$

$\small = 353+(-346) =$

$\small = 353-346 = 7$

220)

$\small 4^{12}÷4^9+2×6+3^2×2×2^2+6^2+5^3-17^2 =$

$\small = 4^{12-9}+12+9×2×4+36+125-289 =$

$\small = 4^3+12+18×4+36+125-289 =$

$\small = 64+12+72+36+125-289 =$

$\small = 309-289 = 20$

221)

$\small 3^3+6^4÷6^2-2^2×3+(3^2)^3÷9^3+30-15-2^2×2^4 =$

$\small = 27+6^{4-2}-4×3+3^{2×3}÷9^3+30-15-2^{2+4} =$

$\small = 27+6^2-12+3^6÷9^3+30-15-2^6 =$

$\small = 27+36-12+\dfrac{3^6}{3^3×3^3}+30-15-64 =$

$\small = 51+3^{6-3-3}+30-15-64 =$

$\small = 51+3^0-49 =$

$\small = 51+1-49 =3$

222)

$\small 54-3^2×4+4×5^2+(3^4+2×6^2)-9^7÷9^5-13^2 =$

$\small 54-9×4+4×25+(81+2×36)-9^{7-5}-169 =$

$\small 54-36+100+(81+72)-9^2-169 =$

$\small 118+153-81-169 =$

$\small (118+153)+(-81-169) =$

$\small 271+(-250) =$

$\small 271-250 = 21$