Question

alguem poderia explicar a questao 2 e 3?

Answer 1

2)
$512 = 2^{9}$
$64 = 2^{6}$
$128 = 2^{7}$
$16 = 2^{4}$
$1024 = 2^{10}$

Portanto:

$\frac{(2^9)^3.(2^6)^6.(2^7)^3}{(2^4)^4.(2^{10})^2} = \frac{2^{12}.2^{12}.2^{10}}{2^8.2^{12}} = \frac{2^{34}}{2^{20}} = 2^{(34-20)} = 2^{14} = 16384$

b)
$0,001 = 10^{-3}$
$1000 = 10^3$
$0,1 = 10^{-1}$
$100 = 10^2$

$\frac{(10^{-3})^3.(10^3)^4.(10^{-1})^{-3}}{(10^{-3})^5.(10^2)^4} = \frac{10^{-6}.10^7.10^{-4}}{10^{-8}.10^6} = \frac{10^{(-6+7-4)}}{10^{(-8+6)}} = \frac{10^{-3}}{10^{-2}} = 10^{(-1)} = 0,1$

3) $\frac{5^{(x+1)}.5^{(x+2)}.5^{(x+3)}}{5^{(x+2)}} = 5^{(x+1+x+3)} = 5^{2(x+2)}} = 25^{(x+2)}$