To solve the expression $\frac{1}{4}$ power of 2 plus $-\frac{1}{2}$ power of 2, we need to interpret it mathematically and evaluate each term step-by-step:

Step 1: Rewrite the terms mathematically

The expression can be rewritten as:

$2^{\frac{1}{4}} + 2^{-\frac{1}{2}}$

Step 2: Evaluate each power of 2

1. Evaluate $2^{\frac{1}{4}}$:

   This means taking the fourth root of 2:

   $2^{\frac{1}{4}} = \sqrt[4]{2} \approx 1.1892$

2. Evaluate $2^{-\frac{1}{2}}$:

   This is equivalent to the reciprocal of the square root of 2:

   $2^{-\frac{1}{2}} = \frac{1}{\sqrt{2}} \approx 0.7071$

Step 3: Add the results

Now add the values obtained from the above calculations:

$2^{\frac{1}{4}} + 2^{-\frac{1}{2}} \approx 1.1892 + 0.7071 = 1.8963$

Final Answer:

$2^{\frac{1}{4}} + 2^{-\frac{1}{2}} \approx 1.8963$

Would you like more details or have any questions?

Related Questions:

1. How do you evaluate expressions with fractional exponents?
2. What is the geometric meaning of fractional exponents?
3. How does the value change if you swap the exponents in the expression?
4. What is the process for simplifying expressions with negative exponents?
5. How can fractional exponents be rewritten as radicals?

Tip: Fractional exponents like $a^{\frac{m}{n}}$ can be thought of as $n$-th roots: $\sqrt[n]{a^m}$.