Question

Se p = $[(2^{-4}.3^5.2^7)^2]^ \frac{3}{4}$, então p é igual a:

a) $2^ \frac{13}{4}.3^ \frac{19}{4}$
b) $2^ \frac{13}{4}.3^ \frac{31}{4}$
c) $2^ \frac{9}{2}.3^ \frac{15}{2}$
d) $2^ \frac{33}{2}.3^ \frac{15}{2}$
e) $2^ \frac{33}{4}.3^ \frac{15}{4}$

Answer 1

P = [ ( 2 ^ -4 * 3 ^ 5 * 2 ^ 7 ) ^ 2 ] ^ 3/4

P = [ 2 ^ -8 * 3 ^ 10 * 2 ^ 14 ] ^ 3 / 4

P = 2 ^ -24/4 * 3 ^ 30/4 * 2 ^ 42/4

P = 3 ^ 30/4 * 2 ^ -24 + 42 / 4

P = 3 ^ 15 / 2 * 2 ^ 18 / 4

P = 3 ^ 15 / 2 * 2 ^ 9 / 2

Alternativa C )

Answer 2

P = [(2^-4 . 3^5.2^7)^2]^3/4

P = [(2^3 . 3^5)^6/4

P =  2^18/4 .3^30/4   ou

P =  2^9/2 .3^15/2    Letra C