Question

Se considera numarul natural n=(5*5la puterea 2 *5la puterea 3)totul la puterea 7/(25la puterea 3)totul la puterea 7.Calculati nla puterea 2017.

Answer 1

Răspuns: n = 1

Salutare!

$\bf n =\dfrac{(5\cdot 5^{2}\cdot 5^{3})^{7}}{(25^{3})^{7}}$

$\bf n =\dfrac{(5^{1}\cdot 5^{2}\cdot 5^{3})^{7}}{25^{3\cdot7}}$

$\bf n =\dfrac{(5^{1+2+3})^{7}}{25^{21}}$

$\bf n =\dfrac{(5^{6})^{7}}{(5^{2})^{21}}$

$\bf n =\dfrac{5^{6\cdot7}}{5^{2\cdot21}}$

$\bf n =\dfrac{5^{42}}{5^{42}}$

$\bf n =5^{42}:5^{42}$

$\bf n =5^{42-42}$

$\bf n =5^{0}$

$\boxed{\bf n =1}$

$\bf n^{2017} = 1^{2017} \implies \boxed{\bf n=1}$

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

==pav38==

Answer 2

Explicație pas cu pas:

Am atasat rezolvarea.....