Question

Se x e y são números reais e 2^x=m/2 e 2^y=n/2, calcule 4^x+y

a) m.n
b) m/n
c) n/m
d) (mm/4)²

Answer 1

$( { {2}^{x} })^{2} = ( { \frac{m}{2} })^{2} \\ {2}^{2x} = \frac{ {m}^{2} }{4} \\ {4}^{x} = \frac{ {m}^{2} }{4}$
De forma análoga
${4}^{y} = \frac{ {n}^{2} }{4}$
Entao multiplicando os dois:
${4}^{x} \times {4}^{y} = \frac{ {m}^{2} }{4} \times \frac{ {n}^{2} }{4} \\ {4}^{x + y} = \frac{ {m}^{2} {n}^{2} }{16} = { (\frac{mn}{4}) }^{2}$