https://file.aiquickdraw.com/mathbot/file/1727616947769lvwkgpqe.jpg

The expression in the image is:

\[
\left( 2 - 2^{\frac{1}{2}} \right)^3
\]

This represents a cube of the term inside the parentheses, where \( 2^{\frac{1}{2}} \) is the square root of 2.

### Step-by-step evaluation:
1. First, calculate \( 2^{\frac{1}{2}} \), which is the square root of 2:
   \[
   2^{\frac{1}{2}} = \sqrt{2} \approx 1.414
   \]

2. Now substitute \( \sqrt{2} \) into the expression inside the parentheses:
   \[
   2 - \sqrt{2} \approx 2 - 1.414 = 0.586
   \]

3. Cube this result:
   \[
   (0.586)^3 = 0.586 \times 0.586 \times 0.586 \approx 0.201
   \]

So, the value of the expression is approximately:

\[
\left( 2 - 2^{\frac{1}{2}} \right)^3 \approx 0.201
\]

Would you like more details on any specific step or further clarification?

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Here are 5 related questions to expand your understanding:

1. How would the result change if the exponent were different, like \( \left( 2 - 2^{\frac{1}{2}} \right)^2 \)?
2. What is the cube root of \( \left( 2 - 2^{\frac{1}{2}} \right)^3 \)?
3. How can you express this using logarithms or exponential notation?
4. How does this equation relate to radical expressions in algebra?
5. How would the result be affected if the base of the exponent was different (e.g., \( 3^{\frac{1}{2}} \))?

**Tip**: Always approximate roots like \( \sqrt{2} \) to several decimal places for more accuracy when working with cubes and higher powers!

Solve the expression (2 - 2^(1/2))^3 with detailed steps. This problem covers exponents, square roots, and cube powers, suitable for Grades 9-11 students. Learn the simplification process and calculation of radical expressions.

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