a)
[tex]\it\dfrac{2^{36}}{2^{38}}= \boxed{\it \dfrac{1}{2^{2}}} \\\\\\2^{36} :2^{38} = 2^{36-38} =2^{-2}[/tex]
b)
[tex]\it\dfrac{3^{54}}{3^{52}}= \boxed{\it 3^{2} } \\\\\\3^{54} :3^{52} = 3^{54-52} =3^{2} = 9[/tex]
c)
[tex]\it \dfrac{4^{16}}{8^{10}}=\dfrac{(2^{2})^{16}}{(2^{3})^{10}}=\dfrac{2^{2\cdot16}}{2^{3\cdot10}}=\dfrac{2^{32}}{2^{30}}=\boxed{\it 2^{2}}} \\\\\\2^{32} :2^{30} = 2^{32-30} =2^{2} = 4[/tex]
d)
[tex]\it\dfrac{27^{5} }{9^{9}}=\dfrac{(3^{3})^{5}}{(3^{2})^{9}}=\dfrac{3^{3\cdot5}}{3^{2\cdot9}}=\dfrac{3^{15}}{3^{18}} = \boxed{\it \dfrac{1}{3^{3}}}\\\\\\\\3^{15} :3^{18} = 3^{15-18}=3^{-3} =\dfrac{1}{3^{3}}[/tex]
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 · 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
- (aⁿ)ᵇ = aⁿ ˣ ᵇ sau aⁿ ˣ ᵇ = (aⁿ) ᵇ
