[tex]\bf (-2)^{100}:[8^{30}:2^{4}+(-10+8)^{36}\cdot 2^{2^{4}}\cdot(-2)^{34}]=[/tex]
[tex]\bf 2^{100}:[(2^{3})^{30}:2^{4}+(-2)^{36}\cdot 2^{16}\cdot2^{34}]=[/tex]
[tex]\bf 2^{100}:(2^{3\cdot30}:2^{4}+2^{36}\cdot 2^{16}\cdot2^{34})=[/tex]
[tex]\bf 2^{100}:(2^{90}:2^{4}+2^{36+16+34})=[/tex]
[tex]\bf 2^{100}:(2^{90-4}+2^{86})=[/tex]
[tex]\bf 2^{100}:(2^{86}+2^{86})=[/tex]
[tex]\bf 2^{100}:(2\cdot 2^{86})=[/tex]
[tex]\bf 2^{100}:2^{1+86}=[/tex]
[tex]\bf 2^{100}:2^{87}=[/tex]
[tex]\bf 2^{100-87}=[/tex]
[tex]\boxed{\bf 2^{13}}[/tex]
Cateva formule pentru puteri
(- a)ⁿ,unde n este o putere impara (-a)ⁿ=(-a)ⁿ
(- a)ⁿ,unde n este o putere para (-a)ⁿ = aⁿ
(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
a⁰ = 1 sau 1 = a⁰
