Question

Por favor galera, ajuda ai.
Diga quais propriedades são necessárias para resolver as seguintes questões. (encontre o valor de y)

a) $2^{2}. 2^{3}=2^{y}$
b) $3^{3} = 9^{y}$
c) $n^{2} . n = n^{2} . n^{y}$
d) $4^{2} . 4 = 4^{2} . 16^{y}$

Answer 1

Em potências, multiplicação de bases iguais e expoentes diferentes, conserva a base e soma os expoentes, feito isso, corta as bases e resolve o que sobrar da equação.

$a) 2^{2}. 2^{3}=2^{y}\to \\\\\\ 2^{5}=2^{y}\to \\\\ 5=y\to \\\\ y=5$




$b) 3^{3} = 9^{y} \to \\\\\\ 3^{3} = 3^{3*y} \to \\\\ 3=3y\to \\\\ y= \frac{3}{3} \to \\\\ y=1$




$c) n^{2} . n = n^{2} . n^{y}\to \\\\\\ n^{2} . n^{1} = n^{2} . n^{y}\to \\\\ n^{3} = n^{2+y}\to \\\\ 3=2+y\to \\\\ 3-2=y\to \\\\ y=1$




$d) 4^{2} . 4 = 4^{2} . 16^{y}\to \\\\\\ 4^{2} . 4^{1} = 4^{2} . 4^{2*y}\to \\\\ 4^{3}= 4^{2+2y}\to \\\\ 3=2+2y\to \\\\ 3-2=2y\to \\\\ 1=2y\to \\\\ \frac{1}{2} =y\to \\\\ y=0,5$

Answer 2

Em potências, multiplicação de bases iguais e expoentes diferentes, conserva a base e soma os expoentes, feito isso, corta as bases e resolve o que sobrar da equação.

$a) 2^{2}. 2^{3}=2^{y}\to \\\\\\ 2^{5}=2^{y}\to \\\\ 5=y\to \\\\ y=5$




$b) 3^{3} = 9^{y} \to \\\\\\ 3^{3} = 3^{3*y} \to \\\\ 3=3y\to \\\\ y= \frac{3}{3} \to \\\\ y=1$




$c) n^{2} . n = n^{2} . n^{y}\to \\\\\\ n^{2} . n^{1} = n^{2} . n^{y}\to \\\\ n^{3} = n^{2+y}\to \\\\ 3=2+y\to \\\\ 3-2=y\to \\\\ y=1$




$d) 4^{2} . 4 = 4^{2} . 16^{y}\to \\\\\\ 4^{2} . 4^{1} = 4^{2} . 4^{2*y}\to \\\\ 4^{3}= 4^{2+2y}\to \\\\ 3=2+2y\to \\\\ 3-2=2y\to \\\\ 1=2y\to \\\\ \frac{1}{2} =y\to \\\\ y=0,5$