Question

Como faz essa função exponencial?

Answer 1

Olá,

na primeira..

$\dfrac{3^{m+1}\cdot9^{m-1}}{27^{m+1}}= \dfrac{3^m\cdot3^1\cdot(3^2)^{m+1}}{(3^3)^{m+1}} \\\\\\ \dfrac{3^{m+1}\cdot9^{m-1}}{27^{m+1}}= \dfrac{3^m\cdot3\cdot3^{2m+2}}{3^{3m+3}}\\\\\\ \dfrac{3^{m+1}\cdot9^{m-1}}{27^{m+1}}= \dfrac{3\cdot3^m\cdot3^{2m}\cdot3^2}{3^{3m}\cdot3^3}\\\\\\ \dfrac{3^{m+1}\cdot9^{m-1}}{27^{m+1}}= \dfrac{9\cdot3\cdot3^{2m+m}}{3^{3m}\cdot27}\\\\\\ \dfrac{3^{m+1}\cdot9^{m-1}}{27^{m+1}}= \dfrac{27\cdot3^{3m}}{27\cdot3^{3m}}$

$\Large \boxed{\dfrac{3^{m+1}\cdot9^{m-1}}{27^{m+1}}= 1}$

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n segunda..

$5^{m+1}+5^{m+2}=5^m\cdot5^1+5^m\cdot5^2\\\\ 5^m~em~evidencia..\\\\ 5^{m+1}+5^{m+2}=5^m\cdot(5+5^2)\\ 5^{m+1}+5^{m+2}=5^m\cdot(5+25)\\\\ \Large\boxed{5^{m+1}+5^{m+2}=30\cdot5^m}$