Question

Pergunta de matemática, Qual o valor de a+b?

Answer 1

Resposta:

$-4$

Explicação passo a passo: Apanhei um pouco, mas consegui resolver a sua questão. Segue a solução.

$\left[\begin{array}{ccc}\frac{2^2\bullet6^4\bullet4^4}{8^6\bullet3}\end{array}\right]^4=2^a\bullet3^b\\\\\\Com\ 6^4=2^4\bullet3^4,\ 4^4=2^4\bullet2^4\ e\ 8^6=2^6\bullet2^6\bullet2^6$

$\left[\begin{array}{ccc}\frac{2^2\bullet2^4\bullet3^4\bullet2^4\bullet2^4}{2^6\bullet2^6\bullet2^6\bullet3}\end{array}\right]^4=2^a\bullet3^b\\\\\\\left[\begin{array}{ccc}\frac{2^6\bullet3^4\bullet2^4\bullet2^2\bullet2^2}{2^6\bullet2^6\bullet2^6\bullet3}\end{array}\right]^4=2^a\bullet3^b$

$\left[\begin{array}{ccc}\frac{2^6\bullet3^4\bullet2^6\bullet2^2}{2^6\bullet2^6\bullet2^6\bullet3}\end{array}\right]^4=2^a\bullet3^b\\\\\\Vamos\ eliminar\ os\ semelhantes:\\\\\left[\begin{array}{ccc}\frac{3^4\bullet2^2}{2^6\bullet3}\end{array}\right]^4=2^a\bullet3^b\\\\\\Temos\ que\ 2^{2-6}=2^{-4}\ e\ 3^{4-1}=3^3\\\\\left[\begin{array}{ccc}2^{-4}\bullet3^3\end{array}\right]^4=2^a\bullet3^b\\\\\\Onde,\ 2^{-4\bullet4}=2^{-16}\ e\ 3^{3\bullet4}=3^{12}\\\\2^{-16}\bullet3^{12}=2^a\bullet3^b$

$Portanto\ a=-16\ e\ b=12.\ Sendo\ a+b=-16+12=-4.$