Question

Przedstaw liczbę w postaci a^m, gdzie m należy do całkowitych.

Answer 1

Niech V będzie symbolem pierwiastka
c) 0,4^7 * 2,5^(-4) / (2/5)^5 = (2/5)^7 * (5/2)^(-4) / (2/5)^5 = (2/5)^2 * (2/5)^4 = (2/5)^6
d) 0,64^5 / (4/5)^(-4) * (4/5)^(-2) = (64/100)^5 / (4/5)^(-4) * (4/5)^(-2) = [(8/10)^2]^5 * (4/5)^4 * (4/5)^(-2) = (4/5)^10 * (4/5)^2 = (4/5)^12
e) V2 * {3}V2 / V8 = 2^(1/2) * 2^(1/3) / 2^(3/2) = 2^(3/6 + 2/6) / 2^(9/6) = 2^(5/6) / 2^(9/6) = 2^(-2/3) = ({3}V2)^(-2)
f) 9^(2/3) * {4}V(27^2) = 3^(4/3) * (27^2)^(1/4) = 3^(4/3) * 27^(1/2) = 3^(4/3) * (3^3)^(1/2) = 3^(4/3) * 3^(3/2) = 3^(8/6 + 9/6) = 3^(17/6) = ({6}V3)^17