Răspuns:
Explicație pas cu pas:
[tex]\bf a=\Big[4^{11}\cdot\big(20\big)^{20}\Big]: \Big [2^{16}\cdot125\cdot\big (2^{5}\big)^{3}\cdot5^{7}\Big]^{2}+2^{3}+\big(7+7^{2}+7^{3}+..+7^{2021}\big)^0[/tex]
[tex]\bf a=\Big[\big(2^{2}\big)^{11}\cdot\big(2^{2}\cdot5\big)^{20}\Big]: \Big [2^{16}\cdot 5^{3}\cdot2^{5\cdot3}\cdot5^{7}\Big]^{2}+2^{3}+1[/tex]
[tex]\bf a=\Big(2^{2\cdot 11}\cdot2^{2\cdot20}\cdot5^{20}\Big): \Big(2^{16}\cdot 5^{3}\cdot2^{15}\cdot5^{7}\Big)^{2}+2^{3}+1[/tex]
[tex]\bf a=\Big(2^{22}\cdot2^{40}\cdot5^{20}\Big): \Big(2^{16+15}\cdot 5^{3+7}\Big)^{2}+8+1[/tex]
[tex]\bf a=\Big(2^{22+40}\cdot5^{20}\Big): \Big (2^{31}\cdot 5^{10}\Big)^{2}+8+1[/tex]
[tex]\bf a=\Big(2^{62}\cdot5^{20}\Big): \Big(2^{31\cdot2}\cdot 5^{10\cdot2} \Big)+8+1[/tex]
[tex]\bf a=\Big(2^{62}\cdot5^{20}\Big): \Big(2^{62}\cdot 5^{20} \Big)+9[/tex]
[tex]\bf a= 1+9[/tex]
[tex]\bf \red{\underline{~a=10~}}[/tex]
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[tex]\bf b=(41^2-82+1) :8:5-(2^6-2^5+2^2-2^0)[/tex]
[tex]\bf b=(1681-82+1) :8:5-(64-32+4-1)[/tex]
[tex]\bf b=1600 :8:5-35[/tex]
[tex]\bf b=200:5-35[/tex]
[tex]\bf b=40-35[/tex]
[tex]\purple{\underline{~\bf b=5~}}[/tex]
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[tex]\bf c=3^{90}-4\cdot9^{44}+2^{208}:\big(2\cdot4^{103}\big)-5\cdot\big(9^{22}\big)^2[/tex]
[tex]\bf c=3^{90}-2^{2} \cdot\big(3^{2}\big)^{44}+2^{208}:\Big[2\cdot\big(2^{2}\big)^{103}\Big]-5\cdot 9^{22\cdot2}[/tex]
[tex]\bf c=3^{90}-2^{2} \cdot 3^{2\cdot44}+2^{208}:\Big(2\cdot2^{2\cdot103}\Big)-5\cdot 9^{44}[/tex]
[tex]\bf c=3^{90}-2^{2} \cdot 3^{88}+2^{208}:\Big(2\cdot2^{206}\Big)-5\cdot \big(3^{2}\big)^{44}[/tex]
[tex]\bf c=3^{90}-2^{2} \cdot 3^{88}+2^{208}:2^{206+1}-5\cdot 3^{2\cdot44}[/tex]
[tex]\bf c=3^{90}-4\cdot 3^{88}+2^{208}:2^{207}-5\cdot 3^{88}[/tex]
[tex]\bf c=3^{90}-4\cdot 3^{88}+2^{208-207}-5\cdot 3^{88}[/tex]
[tex]\bf c=3^{90}-4\cdot 3^{88}+2^{1}-5\cdot 3^{88}[/tex]
[tex]\bf c=3^{90}-9\cdot 3^{88}+2[/tex].
[tex]\bf c=3^{90}-3^{2}\cdot 3^{88}+2[/tex]
[tex]\bf c=3^{90}-3^{2+88}+2[/tex]
[tex]\bf c=3^{90}-3^{90}+2[/tex]
[tex]\pink{\underline{~\bf c=2~}}[/tex]
[tex]==pav38==[/tex]
