Question

(27 1/2*(1/9)3/4)3/4 2) упростите a1/3 b 5/3 a 1/6 b -1/6

Answer 1

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Answer 2

To solve the expression (27 + 1/2 * (1/9)^(3/4))^3/4 + 2, we need to follow the order of operations, which is often remembered as PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, and Addition and Subtraction from left to right).

Let's break down the expression step by step:

Step 1: Evaluate the expression inside the parentheses. - (1/9)^(3/4) can be simplified as the cube root of 1/9 raised to the power of 3/4. - Simplifying further, the cube root of 1/9 can be written as (1/9)^(1/3), and the exponent 3/4 can be written as the square root of (1/9)^(1/3). - Evaluating (1/9)^(1/3) gives us 1/3, and taking the square root gives us 1/sqrt(3).

Step 2: Multiply 1/2 by 1/sqrt(3). - Multiplying 1/2 by 1/sqrt(3) gives us 1/(2*sqrt(3)).

Step 3: Add 27 to the result from Step 2. - Adding 27 to 1/(2*sqrt(3)) gives us 27 + 1/(2*sqrt(3)).

Step 4: Raise the result from Step 3 to the power of 3/4. - Raising (27 + 1/(2*sqrt(3))) to the power of 3/4 gives us (27 + 1/(2*sqrt(3)))^(3/4).

Step 5: Add 2 to the result from Step 4. - Adding 2 to (27 + 1/(2*sqrt(3)))^(3/4) gives us (27 + 1/(2*sqrt(3)))^(3/4) + 2.

Now let's simplify the expression a1/3 + b + 5/3 + a + 1/6 + b - 1/6.

Step 1: Combine like terms. - Combining a1/3 and a gives us (a1/3 + a). - Combining b and b gives us (b + b), which is equal to 2b. - Combining 5/3 and 1/6 gives us (5/3 + 1/6), which is equal to 11/6.

Step 2: Combine the results from Step 1. - Combining (a1/3 + a), 2b, and 11/6 gives us (a1/3 + a + 2b + 11/6).

Therefore, the simplified expression is (27 + 1/(2*sqrt(3)))^(3/4) + 2 + (a1/3 + a + 2b + 11/6).