Răspuns: n = 1
Salutare!
[tex]\bf n =\dfrac{(5\cdot 5^{2}\cdot 5^{3})^{7}}{(25^{3})^{7}}[/tex]
[tex]\bf n =\dfrac{(5^{1}\cdot 5^{2}\cdot 5^{3})^{7}}{25^{3\cdot7}}[/tex]
[tex]\bf n =\dfrac{(5^{1+2+3})^{7}}{25^{21}}[/tex]
[tex]\bf n =\dfrac{(5^{6})^{7}}{(5^{2})^{21}}[/tex]
[tex]\bf n =\dfrac{5^{6\cdot7}}{5^{2\cdot21}}[/tex]
[tex]\bf n =\dfrac{5^{42}}{5^{42}}[/tex]
[tex]\bf n =5^{42}:5^{42}[/tex]
[tex]\bf n =5^{42-42}[/tex]
[tex]\bf n =5^{0}[/tex]
[tex]\boxed{\bf n =1}[/tex]
[tex]\bf n^{2017} = 1^{2017} \implies \boxed{\bf n=1}[/tex]
Cateva 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
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