Question

(2^4/3*2^1/4)^2/12 корень 2

Answer 1

Ответ:

(2 ^ 4 / 3 × 2 ^ 1 / 4) ^ 2 / 12 × √(2) ≅ 0,83

Объяснение:

Answer 2

To simplify the expression (2^4/3 * 2^1/4)^2/12 √2, let's break it down step by step:

Step 1: Simplify the exponent expressions within the parentheses. 2^4/3 can be written as the cube root of 2^4, and 2^1/4 can be written as the fourth root of 2.

(2^4/3 * 2^1/4)^2/12 √2 = (2^(4/3) * 2^(1/4))^2/12 √2 = (2^(4/3 + 1/4))^2/12 √2 = (2^(16/12 + 3/12))^2/12 √2 = (2^(19/12))^2/12 √2

Step 2: Simplify the exponent expression outside the parentheses. (2^(19/12))^2/12 can be simplified as 2^(19/12 * 2/12), which is equal to 2^(38/144).

(2^(19/12))^2/12 √2 = 2^(38/144)/12 √2

Step 3: Simplify the expression under the square root. √2 can be written as 2^(1/2).

2^(38/144)/12 √2 = 2^(38/144)/12 * 2^(1/2) = 2^(38/144 - 12/144) * 2^(1/2) = 2^(26/144) * 2^(1/2) = 2^(26/144 + 72/144) = 2^(98/144)

Therefore, the simplified expression is 2^(98/144).