Question

Considere os números reais a, b e c. Sabendo que a^6=22^4, b^3=22^5 e c^33=22^4, o valor de (a.b.c)^1.222.... é:

Answer 1

a^6 = 22^4 ⇒ a = 22^(4/6)
b^3 = 22^5 ⇒ b = 22^(5/3)
c^33 = 22^4 ⇒ c = 22^(4/33)

(a.b.c) = 22^(4/6) . 22^(5/3) . 22^(4/33)

(a.b.c) = 22^(4/6+5/3+4/33)

(a.b.c) = 22^(162/66)

(a.b.c)^1.222 = (a.b.c)^(11/9)

(a.b.c)^(11/9) = [22^(162/66)]^(11/9)

(a.b.c)^(11/9) = 22^(162/66 * 11/9)

(a.b.c)^(11/9) = 22^(1782/594)

(a.b.c)^(11/9) = 22^3 = 10648