Question

Usando potências de mesma base, e as propriedades das potências, resolva:
A) 2^(m+1) . 2^(m+2) : 4^(m-1)=
B) (0,25)^-1 . (1/4)³=

Answer 1

a) 
$2^{(m+1)} . 2^{(m+2)} : 4^{(m-1)} \\ 2^{(m+1)} . 2^{(m+2)} : (2^{2})^{(m-1)} \\ 2^{m+1+m+2}:2^{2.m-1} \\ 2^{2m+3}:2^{2m-1}\\2^{(2m+3)-(2m-1)}=2^{2m+3-2m+1}=2^{4}=16$

b)
 $(0,25)^{-1} . ( \frac{1}{4})^{3} \\ \\ \frac{25}{100}^{-1}.( \frac{1}{4})^{3} \\ \\ \frac{1}{4}^{-1}. \frac{1}{4}^{3} = \frac{1}{4}^{-1+3}= \frac{1}{4}^{2}= \frac{1}{16}$

Espero ter ajudado! :))