Question

Scrieti ca putere a lui 5

√5/25 * ((0.2) la puterea -1)

(125 la puterea ½) * (25 la puterea ⅔) / (5 la puterea ⅙)

Answer 1

a) radical 5 = 5^(1/2)

25 = 5^2

0,2 = 1/5 => 0,2^(-1) = ((1/5)^(-1) = 1/(1/5) = 5

Atunci: radical 5/25 × (0,2)^(-1) = 5^(1/2)/5^2 × 5 = 5^(1/2)/5^1 = 5^(-1/2)

b) 125 = 5^3 => 125^(1/2) = (5^3)^(1/2) = 5^(3/2)

25 = 5^2 => 25^(2/3) = (5^2)^(2/3) = 5^(4/3)

Atunci: 125^(1/2) × 25^(2/3)/5^(1/6) = 5^(3/2) × 5^(4/3)/5^(1/6) = 5^(3/2 + 4/3 - 1/6) = 5^(9/6+8/6+1/6) = 5^(18/6) = 5^3