Question: $$[ \frac { 2 } { 3 } \div 2 ] \div \frac { 1 } { 3 }$$

Solution

To solve the problem \(\frac{1^{2/3}}{2^{1/3}}\), follow these steps: First, simplify the expression by recognizing the properties of exponents. The expression can be rewritten as: \[ \frac{1^{2/3}}{2^{1/3}} = \frac{1^{2/3}}{2^{1/3}} \] We know that any number raised to any power, \(1^x\), is still 1. So: \[ 1^{2/3} = 1 \] Now the expression becomes: \[ \frac{1}{2^{1/3}} \] Next, calculate \(2^{1/3}\), which is the cube root of 2. Let’s approximate it (or leave it as is because it’s an irrational number). The approximate value of \(2^{1/3}\) is about 1.26. Therefore, the expression is: \[ \frac{1}{1.26} \] The exact answer is: \[ \frac{1}{2^{1/3}} \]