Răspuns:
- [tex]\bf a = 3^{26}[/tex]
- [tex]\bf b = 2^{39}[/tex]
Explicație pas cu pas:
Salutare!
[tex]\bf a = [(2^{3})^{5} +25^{3}-7^{35}:7^{20}):(2^{15}-7^{15}+5^{6}) \cdot 3^{26}[/tex]
[tex]\bf a = [2^{3\cdot5} +(5^{2})^{3}-7^{35-20}):(2^{15}-7^{15}+5^{6})\cdot 3^{26}[/tex]
[tex]\bf a = (2^{15} +5^{2\cdot3}-7^{15}):(2^{15}-7^{15}+5^{6})\cdot 3^{26}[/tex]
[tex]\bf a = (2^{15} +5^{6}-7^{15}):(2^{15}-7^{15}+5^{6})\cdot 3^{26}[/tex]
[tex]\bf a = 1 \cdot 3^{26}[/tex]
[tex]\boxed{ \boxed{ \bf a = 3^{26}}}[/tex]
[tex]\bf b = 2^{101}:[(5^{171}:5^{170}-3)^{98}+2^{105}:(2^{3}\cdot 2^{4})+(2^{11})^{9}]\cdot2^{38}[/tex]
[tex]\bf b = 2^{101}:[(5^{171-170}-3)^{98}+2^{105}:2^{3+4}+2^{11\cdot9}]\cdot2^{38}[/tex]
[tex]\bf b = 2^{101}:[(5^{1}-3)^{98}+2^{105-7}+2^{99}]\cdot2^{38}[/tex]
[tex]\bf b = 2^{101} : (2^{98}+2^{98}+2^{99})\cdot2^{38}[/tex]
[tex]\bf b = 2^{101}:(2\cdot 2^{98}+2^{99})\cdot2^{38}[/tex]
[tex]\bf b = 2^{101}:(2^{98+1}+2^{99})\cdot2^{38}[/tex]
[tex]\bf b = 2^{101}:(2^{99}+2^{99})\cdot2^{38}[/tex]
[tex]\bf b = 2^{101} : 2\cdot 2^{99} \cdot 2^{38}[/tex]
[tex]\bf b = 2^{101} : 2^{99+1} \cdot 2^{38}[/tex]
[tex]\bf b = 2^{101} : 2^{100} \cdot 2^{38}[/tex]
[tex]\bf b = 2^{101 - 100 + 38}[/tex]
[tex]\boxed{\boxed{ \bf b = 2^{39} }}[/tex]
Câteva formule pentru puteri
a⁰ = 1 sau 1 = a⁰
(aⁿ)ᵇ = aⁿ ˣ ᵇ sau aⁿ ˣ ᵇ = (aⁿ)ᵇ
aⁿ · aᵇ = (a · a)ⁿ ⁺ ᵇ sau (a · a)ⁿ ⁺ ᵇ = aⁿ · aᵇ
aⁿ : aᵇ = (a : a)ⁿ ⁻ ᵇ sau (a : a)ⁿ ⁻ ᵇ = aⁿ : aᵇ
aⁿ · bⁿ = (a · b)ⁿ sau (a · b)ⁿ = aⁿ · bⁿ
aⁿ : bⁿ = (a : b)ⁿ sau (a : b)ⁿ = aⁿ : bⁿ
#copaceibrainly
