Let's break down the expression:

\[
\frac{1}{4} \text{ power of } 2 + \frac{-1}{2} \text{ power of } 3
\]

This expression can be rewritten mathematically as:

\[
2^{\frac{1}{4}} + 3^{-\frac{1}{2}}
\]

Now, let's evaluate each term:

1. \( 2^{\frac{1}{4}} \) is the fourth root of 2.
2. \( 3^{-\frac{1}{2}} \) is the negative square root of 3, which can be rewritten as \( \frac{1}{\sqrt{3}} \).

### Calculations:

1. \( 2^{\frac{1}{4}} \approx 1.1892 \)
2. \( 3^{-\frac{1}{2}} \approx \frac{1}{\sqrt{3}} \approx 0.5774 \)

So, the expression becomes:

\[
2^{\frac{1}{4}} + 3^{-\frac{1}{2}} \approx 1.1892 + 0.5774 = 1.7666
\]

Therefore, the value of the expression is approximately **1.7666**.

Would you like more details or have any questions? 

Here are some related questions:

1. What is the cube root of 2?
2. How do you calculate fractional exponents?
3. What is the value of \( 5^{\frac{1}{3}} \)?
4. How do negative exponents affect the value of a number?
5. How does \( 2^{\frac{1}{2}} \) compare to \( 3^{\frac{1}{2}} \)?

**Tip:** When dealing with fractional exponents, remember that the numerator indicates the power, and the denominator indicates the root.

Learn how to evaluate the expression 1/4 power of 2 + -1/2 power of 3. This problem involves understanding fractional exponents, roots, and applying the negative exponent rule. Suitable for students in Grades 9-10.

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