Question

O valor de [4^7.4^10.4]2: (4^5)7 é:

Answer 1

Olá, bom dia!

Vou colocar as propriedades que vamos utilizar:

$a^m\cdot a^n=a^{m+n}\\\\(a^n)^m=a^{n\cdot m}\\\\\dfrac{a^m}{a^n}=a^{m-n}$

Agora é só utilizá-las:

$\dfrac{(4^7\cdot4^{10}\cdot4)^2}{(4^5)^7}=\\\\\\\dfrac{(4^{7+10+1})^2}{4^{5\cdot7}}=\\\\\\\dfrac{(4^{18})^2}{4^{35}}=\\\\\\\dfrac{4^{18\cdot2}}{4^{35}}=\\\\\\\dfrac{4^{36}}{4^{35}}=\\\\\\4^{36-35}=\\\\\\\boxed{4^1=4}$

Espero ter ajudado.

Bons estudos! :)