Question

Solve [3 ÷ (2 * 1)]^(2/3).
A) 1
B) 27
C) 8
D) 64/27

Answer 1

The expression [3 ÷ (2 * 1)]^(2/3) simplifies to 1.5^(2/3). After squaring 1.5 and taking the cube root, the result does not match any of the options exactly but is closest to 1, which is option A.

Step-by-step explanation:

To solve the provided expression [3 ÷ (2 * 1)]^(2/3), we first simplify the expression inside the parentheses and then apply the exponent. Let's break it down step-by-step:

1. Simplify inside the parentheses: 3 ÷ (2 * 1) = 3 ÷ 2 = 1.5
2. Raise this result to the power of 2/3: (1.5)^(2/3). We can interpret this as the cube root of 1.5 squared. To perform this operation without a calculator, it can be quite challenging, but we can approximate or use a calculator for precise results.
3. Calculating the cube root of 1.5 and then squaring it is the same as squaring 1.5 and taking the cube root: (1.5^2)^(1/3) which equals (2.25)^(1/3).
4. Approximate or use a calculator to find the cube root of 2.25. It will not precisely match any of the answer choices, but it is closest to 1, which is option A.

Therefore, the correct answer is option A, which is 1. (A)